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Fei J, Ren S, Zheng C, Yu J, Hu C. Aperiodically intermittent quantized control-based exponential synchronization of quaternion-valued inertial neural networks. Neural Netw 2024; 180:106669. [PMID: 39226851 DOI: 10.1016/j.neunet.2024.106669] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2024] [Revised: 08/03/2024] [Accepted: 08/26/2024] [Indexed: 09/05/2024]
Abstract
Inertial neural networks are proposed via introducing an inertia term into the Hopfield models, which make their dynamic behavior more complex compared to the traditional first-order models. Besides, the aperiodically intermittent quantized control over conventional feedback control has its potential advantages on reducing communication blocking and saving control cost. Based on these facts, we are mainly devoted to exploring of exponential synchronization of quaternion-valued inertial neural networks under aperiodically intermittent quantized control. Firstly, a compact quaternion-valued aperiodically intermittent quantized control protocol is developed, which can mitigate significantly the complexity of theoretical derivation. Subsequently, several concise criteria involving matrix inequalities are formulated through constructing a type of Lyapunov functional and employing a direct analysis approach. The correctness of the obtained results eventually is verified by a typical example.
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Affiliation(s)
- Jingnan Fei
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China.
| | - Sijie Ren
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China.
| | - Caicai Zheng
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China.
| | - Juan Yu
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China; Xinjiang Key Laboratory of Applied Mathematics (XJDX1401), Urumqi, 830017, China.
| | - Cheng Hu
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China; Xinjiang Key Laboratory of Applied Mathematics (XJDX1401), Urumqi, 830017, China.
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2
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Zheng C, Hu C, Yu J, Wen S. Saturation function-based continuous control on fixed-time synchronization of competitive neural networks. Neural Netw 2024; 169:32-43. [PMID: 37857171 DOI: 10.1016/j.neunet.2023.10.008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2023] [Revised: 09/17/2023] [Accepted: 10/06/2023] [Indexed: 10/21/2023]
Abstract
Currently, through proposing discontinuous control strategies with the signum function and discussing separately short-term memory (STM) and long-term memory (LTM) of competitive artificial neural networks (ANNs), the fixed-time (FXT) synchronization of competitive ANNs has been explored. Note that the method of separate analysis usually leads to complicated theoretical derivation and synchronization conditions, and the signum function inevitably causes the chattering to reduce the performance of the control schemes. To try to solve these challenging problems, the FXT synchronization issue is concerned in this paper for competitive ANNs by establishing a theorem of FXT stability with switching type and developing continuous control schemes based on a kind of saturation functions. Firstly, different from the traditional method of studying separately STM and LTM of competitive ANNs, the models of STM and LTM are compressed into a high-dimensional system so as to reduce the complexity of theoretical analysis. Additionally, as an important theoretical preliminary, a FXT stability theorem with switching differential conditions is established and some high-precision estimates for the convergence time are explicitly presented by means of several special functions. To achieve FXT synchronization of the addressed competitive ANNs, a type of continuous pure power-law control scheme is developed via introducing the saturation function instead of the signum function, and some synchronization criteria are further derived by the established FXT stability theorem. These theoretical results are further illustrated lastly via a numerical example and are applied to image encryption.
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Affiliation(s)
- Caicai Zheng
- College of Mathematics and System Science, Xinjiang University, Urumqi, 830017, China.
| | - Cheng Hu
- College of Mathematics and System Science, Xinjiang University, Urumqi, 830017, China; Xinjiang Key Laboratory of Applied Mathematics, Urumqi, 830017, China.
| | - Juan Yu
- College of Mathematics and System Science, Xinjiang University, Urumqi, 830017, China; Xinjiang Key Laboratory of Applied Mathematics, Urumqi, 830017, China.
| | - Shiping Wen
- Centre for Artificial Intelligence, University of Technology Sydney, Ultimate 2007, Australia.
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3
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Pu H, Li F, Wang Q, Li P. Preassigned-time projective synchronization of delayed fully quaternion-valued discontinuous neural networks with parameter uncertainties. Neural Netw 2023; 165:740-754. [PMID: 37406427 DOI: 10.1016/j.neunet.2023.06.017] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2023] [Revised: 05/19/2023] [Accepted: 06/08/2023] [Indexed: 07/07/2023]
Abstract
This paper concerns with the preassigned-time projective synchronization issue for delayed fully quaternion-valued discontinuous neural networks involving parameter uncertainties through the non-separation method. Above all, based on the existing works, a new preassigned-time stability theorem is established. Subsequently, to realize the control goals, two types of novel and simple chattering-free quaternion controllers are designed, one without the power-law term and the other with a hyperbolic-tangent function. They are different from the existing common power-law controller and exponential controller. Thirdly, under the Filippov discontinuity theories and with the aid of quaternion inequality techniques, some novel succinct sufficient criteria are obtained to ensure the addressed systems to achieve the preassigned-time synchronization by using the preassigned-time stability theory. The preassigned settling time is free from any parameter and any initial value of the system, and can be preset according to the actual task demands. Particularly, unlike the existing results, the proposed control methods can effectively avoid the chattering phenomenon, and the time delay part is removed for simplicity. Additionally, the projection coefficient is generic quaternion-valued instead of real-valued or complex-valued, and some of the previous relevant results are extended. Lastly, numerical simulations are reported to substantiate the effectiveness of the control strategies, the merits of preassigned settling time, and the correctness of the acquired results.
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Affiliation(s)
- Hao Pu
- School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, China
| | - Fengjun Li
- School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, China.
| | - Qingyun Wang
- School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, China; School of Aeronautic Science and Engineering, Beihang University, Beijing, 100191, China
| | - Pengzhen Li
- Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, 60607, USA
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4
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Wang X, Cao J, Zhou X, Liu Y, Yan Y, Wang J. A novel framework of prescribed time/fixed time/finite time stochastic synchronization control of neural networks and its application in image encryption. Neural Netw 2023; 165:755-773. [PMID: 37418859 DOI: 10.1016/j.neunet.2023.06.023] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2022] [Revised: 05/27/2023] [Accepted: 06/19/2023] [Indexed: 07/09/2023]
Abstract
In this paper, we investigate a novel framework for achieving prescribed-time (PAT), fixed-time (FXT) and finite-time (FNT) stochastic synchronization control of semi-Markov switching quaternion-valued neural networks (SMS-QVNNs), where the setting time (ST) of PAT/FXT/FNT stochastic synchronization control is effectively preassigned beforehand and estimated. Different from the existing frameworks of PAT/FXT/FNT control and PAT/FXT control (where PAT control is deeply dependent on FXT control, meaning that if the FXT control task is removed, it is impossible to implement the PAT control task), and different from the existing frameworks of PAT control (where a time-varying control gain such as μ(t)=T/(T-t) with t∈[0,T) was employed, leading to an unbounded control gain as t→T- from the initial time to prescribed time T), the investigated framework is only built on a control strategy, which can accomplish its three control tasks (PAT/FXT/FNT control), and the control gains are bounded even though time t tends to the prescribed time T. Four numerical examples and an application of image encryption/decryption are given to illustrate the feasibility of our proposed framework.
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Affiliation(s)
- Xin Wang
- School of Computer Science and Technology, Huaiyin Normal University, Huaian 223300, Jiangsu, China; Huai'an Key Laboratory of Big Data Intelligent Computing and Analysis, Huaiyin Normal University, Huaian 223300, Jiangsu, China.
| | - Jinde Cao
- School of Mathematics, Southeast University, Nanjing 210096, Jiangsu, China; Yonsei Frontier Lab, Yonsei University, Seoul 03722, South Korea
| | - Xianghui Zhou
- School of Mathematics and Statistics, Anhui Normal University, Wuhu 241000, Anhui, China
| | - Ying Liu
- School of Mathematics and Statistics, Huaiyin Normal University, Huaian 223300, Jiangsu, China
| | - Yaoxi Yan
- School of Computer Science and Technology, Huaiyin Normal University, Huaian 223300, Jiangsu, China; Huai'an Key Laboratory of Big Data Intelligent Computing and Analysis, Huaiyin Normal University, Huaian 223300, Jiangsu, China
| | - Jiangtao Wang
- School of Computer Science and Technology, Huaiyin Normal University, Huaian 223300, Jiangsu, China; Huai'an Key Laboratory of Big Data Intelligent Computing and Analysis, Huaiyin Normal University, Huaian 223300, Jiangsu, China
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5
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Bao Y, Zhang Y, Zhang B. Resilient fixed-time stabilization of switched neural networks subjected to impulsive deception attacks. Neural Netw 2023; 163:312-326. [PMID: 37094518 DOI: 10.1016/j.neunet.2023.04.003] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2022] [Revised: 02/25/2023] [Accepted: 04/02/2023] [Indexed: 04/26/2023]
Abstract
This article focuses on the resilient fixed-time stabilization of switched neural networks (SNNs) under impulsive deception attacks. A novel theorem for the fixed-time stability of impulsive systems is established by virtue of the comparison principle. Existing fixed-time stability theorems for impulsive systems assume that the impulsive strength is not greater than 1, while the proposed theorem removes this assumption. SNNs subjected to impulsive deception attacks are modeled as impulsive systems. Some sufficient criteria are derived to ensure the stabilization of SNNs in fixed time. The estimation of the upper bound for the settling time is also given. The influence of impulsive attacks on the convergence time is discussed. A numerical example and an application to Chua's circuit system are given to demonstrate the effectiveness of the theoretical results.
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Affiliation(s)
- Yuangui Bao
- School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, People's Republic of China; School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, People's Republic of China; Yangtze Delta Region Academy of Beijing Institute of Technology, Jiaxing 314000, People's Republic of China.
| | - Yijun Zhang
- School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, People's Republic of China.
| | - Baoyong Zhang
- School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, People's Republic of China.
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6
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Wei R, Cao J, Alsaadi FE. Fixed/Prescribed-Time Bipartite Synchronization of Coupled Quaternion-Valued neural Networks with Competitive Interactions. Neural Process Lett 2023. [DOI: 10.1007/s11063-023-11225-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/29/2023]
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7
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Yang J, Chen G, Zhu S, Wen S, Hu J. Fixed/prescribed-time synchronization of BAM memristive neural networks with time-varying delays via convex analysis. Neural Netw 2023; 163:53-63. [PMID: 37028154 DOI: 10.1016/j.neunet.2023.03.031] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2022] [Revised: 02/26/2023] [Accepted: 03/21/2023] [Indexed: 03/29/2023]
Abstract
The synchronization problem of bidirectional associative memory memristive neural networks (BAMMNNs) with time-varying delays plays an essential role in the implementation and application of neural networks. Firstly, under the framework of the Filippov's solution, the discontinuous parameters of the state-dependent switching are transformed by convex analysis method, which is different from most previous approaches. Secondly, based on Lyapunov function and some inequality techniques, several conditions for the fixed-time synchronization (FXTS) of the drive-response systems are obtained by designing special control strategies. Moreover, the settling time (ST) is estimated by the improved fixed-time stability lemma. Thirdly, the driven-response BAMMNNs are investigated to be synchronized within a prescribed time by designing new controllers based on the FXTS results, where ST is irrelevant to the initial values of BAMMNNs and the parameters of controllers. Finally, a numerical simulation is exhibited to verify the correctness of the conclusions.
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Affiliation(s)
- Jinrong Yang
- College of Science, Wuhan University of Science and Technology, Wuhan 430065, China; Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan 430065, China.
| | - Guici Chen
- College of Science, Wuhan University of Science and Technology, Wuhan 430065, China; Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan 430065, China.
| | - Song Zhu
- School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, China.
| | - Shiping Wen
- Centre for Artificial Intelligence, University of Technology Sydney, Sydney, 2007, Australia.
| | - Junhao Hu
- School of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074, China.
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8
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Zhou X, Cao J, Wang X. Predefined-time synchronization of coupled neural networks with switching parameters and disturbed by Brownian motion. Neural Netw 2023; 160:97-107. [PMID: 36623446 DOI: 10.1016/j.neunet.2022.12.024] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2022] [Revised: 12/22/2022] [Accepted: 12/30/2022] [Indexed: 01/05/2023]
Abstract
This article focuses on predefined time synchronization problem for a class of signal switching neural networks with time-varying delays. In the network models, we not only consider the coupling characteristics in the following networks, but also consider the disturbance with standard Brownian motion. In the design of the controller, the control gain is designed as 1ɛ+Tp-t (t∈[T0,Tp), ɛ is an optional smaller positive number), which avoids the infinite gain (the control gain is designed as 1Tp-t in other reference). In order to get the predefined time control law, a power function is multiplied to the Lyapunov functional, from which it can get an exponential upper bound function via the derivative and mathematical expectation operation. Utilizing the martingale theory and the method of Laplace matrix, some novel predefined time synchronization criteria are obtained for the leader-following neural networks, meanwhile the following networks can maintain the leader network after achieved synchronization. Based on the special network of the main system, five corollaries separately develop the predefined time synchronization results from different perspectives. An example with some simulation figures and computing results fully exhibits the effectiveness of the achieved synchronization scheme. In this case, although the error signal is disturbed by Brownian motion, the trace signal can still stably converge to zero by this control scheme, meanwhile the predefined-time control effect is achieved.
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Affiliation(s)
- Xianghui Zhou
- School of Mathematics and Statistics, Anhui Normal University, Wuhu 241000, Anhui, China.
| | - Jinde Cao
- School of Mathematics, Southeast University, Nanjing 210096, China; Yonsei Frontier Lab, Yonsei University, Seoul, 03722, South Korea.
| | - Xin Wang
- School of Computer Science and Technology, Huaiyin Normal University, Huaian 223300, Jiangsu, China.
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9
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Peng T, Wu Y, Tu Z, Alofi AS, Lu J. Fixed-time and prescribed-time synchronization of quaternion-valued neural networks: A control strategy involving Lyapunov functions. Neural Netw 2023; 160:108-121. [PMID: 36630738 DOI: 10.1016/j.neunet.2022.12.014] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2022] [Revised: 11/26/2022] [Accepted: 12/19/2022] [Indexed: 01/05/2023]
Abstract
A control strategy containing Lyapunov functions is proposed in this paper. Based on this strategy, the fixed-time synchronization of a time-delay quaternion-valued neural network (QVNN) is analyzed. This strategy is extended to the prescribed-time synchronization of the QVNN. Furthermore, an improved two-step switching control strategy is also proposed based on this flexible control strategy. Compared with some existing methods, the main method of this paper is a non-decomposition one, does not contain a sign function in the controller, and has better synchronization accuracy. Two numerical examples verify the above advantages.
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Affiliation(s)
- Tao Peng
- School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404100, China; Department of Systems Science, School of Mathematics, Southeast University, Nanjing 210096, China.
| | - Yanqiu Wu
- School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404100, China.
| | - Zhengwen Tu
- School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404100, China.
| | - A S Alofi
- Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia.
| | - Jianquan Lu
- Department of Systems Science, School of Mathematics, Southeast University, Nanjing 210096, China; School of Automation and Electrical Engineering, Linyi University, Linyi 276005, China.
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10
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Qin X, Jiang H, Qiu J, Hu C, Ren Y. Strictly intermittent quantized control for fixed/predefined-time cluster lag synchronization of stochastic multi-weighted complex networks. Neural Netw 2023; 158:258-271. [PMID: 36481458 DOI: 10.1016/j.neunet.2022.10.033] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2022] [Revised: 08/27/2022] [Accepted: 10/31/2022] [Indexed: 11/21/2022]
Abstract
This article addresses the fixed-time (F-T) and predefined-time (P-T) cluster lag synchronization of stochastic multi-weighted complex networks (SMWCNs) via strictly intermittent quantized control (SIQC). Firstly, by exploiting mathematical induction and reduction to absurdity, a novel F-T stability lemma is proved and an accurate estimation of settling time (ST) is obtained. Subsequently, by virtue of the proposed F-T stability, some simple conditions that ensure the F-T cluster lag synchronization of SMWCNs are derived by developing a SIQC strategy. Furthermore, the P-T cluster lag synchronization is also explored based on a SIQC design, where the ST can be predefined by an adjustable constant of the controller. Note that the designed controllers here are simpler and more economical than the traditional design whose the linear part is still activated during the rest interval. Finally, two numerical examples are provided to verify the effectiveness of the theoretical results.
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Affiliation(s)
- Xuejiao Qin
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, PR China
| | - Haijun Jiang
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, PR China.
| | - Jianlong Qiu
- School of Automation and Electrical Engineering, Linyi University, Linyi 276005, PR China
| | - Cheng Hu
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, PR China
| | - Yue Ren
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, PR China
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11
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Liu Y, Wang X, Zhou X, Cao J. A Novel Control Law Design for Prescribed-Time/Fixed-Time Stochastic Synchronization Control of Neural Networks. ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2022. [DOI: 10.1007/s13369-022-07499-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/04/2022]
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12
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Finite-time stabilization of quaternion-valued neural networks with time delays: An implicit function method. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2022.09.014] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
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13
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Mao X, Wang X, Qin H. Stability analysis of quaternion-valued BAM neural networks fractional-order model with impulses and proportional delays. Neurocomputing 2022. [DOI: 10.1016/j.neucom.2022.08.059] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/15/2022]
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14
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Wei R, Cao J. Prespecified-time bipartite synchronization of coupled reaction-diffusion memristive neural networks with competitive interactions. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:12814-12832. [PMID: 36654023 DOI: 10.3934/mbe.2022598] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
In this paper, we investigate the prespecified-time bipartite synchronization (PTBS) of coupled reaction-diffusion memristive neural networks (CRDMNNs) with both competitive and cooperative interactions. Two types of bipartite synchronization are considered: leaderless PTBS and leader-following PTBS. With the help of a structural balance condition, the criteria for PTBS for CRDMNNs are derived by designing suitable Lyapunov functionals and novel control protocols. Different from the traditional finite-time or fixed-time synchronization, the settling time obtained in this paper is independent of control gains and initial values, which can be pre-set according to the task requirements. Lastly, numerical simulations are given to verify the obtained results.
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Affiliation(s)
- Ruoyu Wei
- School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
| | - Jinde Cao
- School of Mathematics, Southeast University, Nanjing 210096, China
- Yonsei Frontier Lab, Yonsei University, Seoul 03722, South Korea
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15
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Fixed/Preassigned-time synchronization of high-dimension-valued fuzzy neural networks with time-varying delays via nonseparation approach. Knowl Based Syst 2022. [DOI: 10.1016/j.knosys.2022.109774] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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16
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Aperiodically Intermittent Control for Exponential Stabilization of Delayed Neural Networks Via Time-dependent Functional Method. Neural Process Lett 2022. [DOI: 10.1007/s11063-022-10943-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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17
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Wu Q, Yao Z, Yin Z, Zhang H. Fin-TS and Fix-TS on fractional quaternion delayed neural networks with uncertainty via establishing a new Caputo derivative inequality approach. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:9220-9243. [PMID: 35942756 DOI: 10.3934/mbe.2022428] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
This paper investigates the finite time synchronization (Fin-TS) and fixed time synchronization (Fix-TS) issues on Caputo quaternion delayed neural networks (QDNNs) with uncertainty. A new Caputo fractional differential inequality is constructed, then Fix-TS settling time of the positive definite function is estimated, which is very convenient to derive Fix-TS condition to Caputo QDNNs. By designing the appropriate self feedback and adaptive controllers, the algebraic discriminant conditions to achieve Fin-TS and Fix-TS on Caputo QDNNs are proposed based on quaternion direct method, Lyapunov stability theory, extended Cauchy Schwartz inequality, Jensen inequality. Finally, the correctness and validity of the presented results under the different orders are verified by two numerical examples.
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Affiliation(s)
- Qiong Wu
- School of Mathematics and Physics, Anqing Normal University, Anqing 246133, China
| | - Zhimin Yao
- School of Mathematics and Physics, Anqing Normal University, Anqing 246133, China
| | - Zhouping Yin
- School of Mathematics and Physics, Anqing Normal University, Anqing 246133, China
| | - Hai Zhang
- School of Mathematics and Physics, Anqing Normal University, Anqing 246133, China
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18
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Zheng C, Hu C, Yu J, Jiang H. Fixed-time synchronization of discontinuous competitive neural networks with time-varying delays. Neural Netw 2022; 153:192-203. [PMID: 35738144 DOI: 10.1016/j.neunet.2022.06.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2022] [Revised: 05/25/2022] [Accepted: 06/01/2022] [Indexed: 10/18/2022]
Abstract
In this article, the fixed-time (FXT) synchronization of discontinuous competitive neural networks (CNNs) involving time-varying delays is investigated. Firstly, two kinds of discontinuous FXT control schemes are proposed and two forms of Lyapunov function are constructed based on p-norm and 1-norm to discuss the FXT synchronization of CNNs. By means of nonsmooth analysis and some inequality techniques, some simple criteria are obtained to achieve FXT synchronization and the upper bound of the settling time with less conservativeness is provided. Furthermore, the effect of time scale on FXT synchronization of CNNs is considered. Lastly, some numerical results for an example are provided to demonstrate the derived theoretical results.
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Affiliation(s)
- Caicai Zheng
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China.
| | - Cheng Hu
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China.
| | - Juan Yu
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China.
| | - Haijun Jiang
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China.
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