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Bao B, Hu J, Bao H, Xu Q, Chen M. Memristor-coupled dual-neuron mapping model: initials-induced coexisting firing patterns and synchronization activities. Cogn Neurodyn 2024; 18:539-555. [PMID: 38699613 PMCID: PMC11061084 DOI: 10.1007/s11571-023-10006-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2023] [Revised: 07/25/2023] [Accepted: 08/24/2023] [Indexed: 05/05/2024] Open
Abstract
Synaptic plasticity makes memristors particularly suitable for simulating the connection synapses between neurons that describe magnetic induction coupling. By applying a memristor to the synaptic coupling between two map-based neuron models, a memristor-coupled dual-neuron mapping (MCDN) model is proposed in this article. The MCDN model has a line fixed point set associated with the memristor initial state, which is always unstable for the model parameters and memristor initial state of interest. Complex spiking/bursting firing patterns and their transitions are disclosed using some dynamical analysis means. The numerical results show that these spiking/bursting firings are significantly relied on the memristor initial state, demonstrating the coexistence of firing patterns. Moreover, the initial effects of complete synchronization are explored for the homogeneous MCDN model, and it is clarified that in addition to being related to the coupling strength, the synchronization activities are extremely dependent on the initial states of the memristor and neurons. Finally, these numerical results are confirmed by the FPGA-based hardware experiments.
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Affiliation(s)
- Bocheng Bao
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213159 People’s Republic of China
| | - Jingting Hu
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213159 People’s Republic of China
| | - Han Bao
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213159 People’s Republic of China
| | - Quan Xu
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213159 People’s Republic of China
| | - Mo Chen
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213159 People’s Republic of China
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Alexander P, Parastesh F, Hamarash II, Karthikeyan A, Jafari S, He S. Effect of the electromagnetic induction on a modified memristive neural map model. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:17849-17865. [PMID: 38052539 DOI: 10.3934/mbe.2023793] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/07/2023]
Abstract
The significance of discrete neural models lies in their mathematical simplicity and computational ease. This research focuses on enhancing a neural map model by incorporating a hyperbolic tangent-based memristor. The study extensively explores the impact of magnetic induction strength on the model's dynamics, analyzing bifurcation diagrams and the presence of multistability. Moreover, the investigation extends to the collective behavior of coupled memristive neural maps with electrical, chemical, and magnetic connections. The synchronization of these coupled memristive maps is examined, revealing that chemical coupling exhibits a broader synchronization area. Additionally, diverse chimera states and cluster synchronized states are identified and discussed.
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Affiliation(s)
- Prasina Alexander
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai, India
| | - Fatemeh Parastesh
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Iran
| | - Ibrahim Ismael Hamarash
- Electrical Engineering Department, Salahaddin University-Erbil, Kirkuk Rd., Erbil, Kurdistan, Iraq
- School of Computer Science and Engineering, University of Kurdistan Hewler, 40m St., Erbil, Kurdistan, Iraq
| | - Anitha Karthikeyan
- Department of Electronics and Communication Engineering, Vemu Institute of Technology, Chithoor, India
- Department of Electronics and Communications Engineering and University Centre for Research & Development, Chandigarh University, Mohali-140413, Punjab
| | - Sajad Jafari
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Iran
- Health Technology Research Institute, Amirkabir University of Technology (Tehran Polytechnic), Iran
| | - Shaobo He
- School of Automation and Electronic Information, Xiangtan University, Xiangtan 411105, China
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Xu Q, Liu T, Ding S, Bao H, Li Z, Chen B. Extreme multistability and phase synchronization in a heterogeneous bi-neuron Rulkov network with memristive electromagnetic induction. Cogn Neurodyn 2023; 17:755-766. [PMID: 37265650 PMCID: PMC10229522 DOI: 10.1007/s11571-022-09866-3] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2022] [Revised: 07/13/2022] [Accepted: 07/18/2022] [Indexed: 11/03/2022] Open
Abstract
Memristive electromagnetic induction effect has been widely explored in bi-neuron network with homogeneous neurons, but rarely in bi-neuron network with heterogeneous ones. This paper builds a bi-neuron network by coupling heterogeneous Rulkov neurons with memristor and investigates the memristive electromagnetic induction effect. Theoretical analysis discloses that the bi-neuron network possesses a line equilibrium state and its stability depends on the memristor coupling strength and initial condition. That is, the stability of the line equilibrium state has a transition between unstable saddle-focus and stable node-focus via Hopf bifurcation. By employing parameters located in the stable node-focus region, dynamical behaviors related to the memristor coupling strength and initial conditions are revealed by Julia- and MATLAB-based multiple numerical tools. Numerical results demonstrate that the proposed heterogeneous bi-neuron Rulkov network can generate point attractor, period, chaos, chaos crisis, and period-doubling bifurcation. Note that extreme multistability are disclosed with respect to initial conditions of memristor and gated ion concentration. Coexisting infinitely multiple firing patterns of periodic firing patterns with different periodicities and chaotic firing patterns for different memristor initial conditions are demonstrated by phase portrait and time-domain waveform. Besides, the phase synchronization related to the memristor coupling strength and its initial condition is explored, which suggests that the two heterogeneous neurons become phase synchronization with large memristor coupling strength and initial condition. This also reflects that the plasticity of memristor synapse enables adaptive regulation in keeping energy balance between the neurons. What's more, MCU-based hardware experiments are executed to further confirm the numerical simulations.
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Affiliation(s)
- Quan Xu
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213164 China
| | - Tong Liu
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213164 China
| | - Shoukui Ding
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213164 China
| | - Han Bao
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213164 China
| | - Ze Li
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213164 China
| | - Bei Chen
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213164 China
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Wang G, Fu Y. Spatiotemporal patterns and collective dynamics of bi-layer coupled Izhikevich neural networks with multi-area channels. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:3944-3969. [PMID: 36899611 DOI: 10.3934/mbe.2023184] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
The firing behavior and bifurcation of different types of Izhikevich neurons are analyzed firstly through numerical simulation. Then, a bi-layer neural network driven by random boundary is constructed by means of system simulation, in which each layer is a matrix network composed of 200 × 200 Izhikevich neurons, and the bi-layer neural network is connected by multi-area channels. Finally, the emergence and disappearance of spiral wave in matrix neural network are investigated, and the synchronization property of neural network is discussed. Obtained results show that random boundary can induce spiral waves under appropriate conditions, and it is clear that the emergence and disappearance of spiral wave can be observed only when the matrix neural network is constructed by regular spiking Izhikevich neurons, while it cannot be observed in neural networks constructed by other modes such as fast spiking, chattering and intrinsically bursting. Further research shows that the variation of synchronization factor with coupling strength between adjacent neurons shows an inverse bell-like curve in the form of "inverse stochastic resonance", but the variation of synchronization factor with coupling strength of inter-layer channels is a curve that is approximately monotonically decreasing. More importantly, it is found that lower synchronicity is helpful to develop spatiotemporal patterns. These results enable people to further understand the collective dynamics of neural networks under random conditions.
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Affiliation(s)
- Guowei Wang
- School of Education, Nanchang Institute of Science and Technology, Nanchang 330108, China
| | - Yan Fu
- School of Mathematics and Computer Science, Yuzhang Normal University, Nanchang 330108, China
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Zhang S, Yang Y, Sui X, Zhang Y. Synchronization of fractional-order memristive recurrent neural networks via aperiodically intermittent control. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:11717-11734. [PMID: 36124610 DOI: 10.3934/mbe.2022545] [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
In this paper, synchronization of fractional-order memristive recurrent neural networks via aperiodically intermittent control is investigated. Considering the special properties of memristor neural network, differential inclusion theory is introduced. Similar to the aperiodically strategy of integer order, aperiodically intermittent control strategy of fractional order is proposed. Under the framework of Fillipov's solution, based on the intermittent strategy of fractional order systems and the properties Mittag-Leffler, sufficient criteria of aperiodically intermittent strategy are obtained by constructing appropriate Lyapunov functional. Some comparisons are given to demonstrate the advantages of aperiodically strategy. A simulation example is given to illustrate the derived conclusions.
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Affiliation(s)
- Shuai Zhang
- College of Computer and Information Engineering, Henan Normal University, Xinxiang 453007, China
- Engineering Lab of Intelligence Business & Internet of Things, Henan Province, Xinxiang 453007, China
- College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China
| | - Yongqing Yang
- School of Science, Jiangnan University, Wuxi 214122, China
| | - Xin Sui
- School of Mathematics and Information Sciences, Yantai University, Yantai 264005, China
| | - Yanna Zhang
- College of Computer and Information Engineering, Henan Normal University, Xinxiang 453007, China
- Engineering Lab of Intelligence Business & Internet of Things, Henan Province, Xinxiang 453007, China
- College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China
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Lu Y, Wang C, Deng Q. Rulkov neural network coupled with discrete memristors. NETWORK (BRISTOL, ENGLAND) 2022; 33:214-232. [PMID: 36200906 DOI: 10.1080/0954898x.2022.2131921] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2022] [Revised: 09/15/2022] [Accepted: 09/26/2022] [Indexed: 06/16/2023]
Abstract
The features of memristive-coupled neural networks have been studied extensively in the continuous field. However, the particularities of the discrete domain are rarely mentioned. This paper constructs a discrete memristor with sine-type conductance and applies the discrete memristor to coupling the Rulkov neuron maps for the first time. The properties of the proposed memristive-coupled bi-neuron Rulkov map and multi-neuron Rulkov neural network are probed. In order to better characterize the discrete system, many numerical simulation methods are used. Such as the normalized mean synchronization error, bifurcation diagrams, phase portraits, spatiotemporal patterns and so on. Numerical studies have shown that in discrete memristor-coupled neural networks, both parameters and coupling factors affect the dynamics of the system, resulting in complex and interesting behavioural changes.
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Affiliation(s)
- Yanmei Lu
- College of Computer Science and Electronic Engineering, Hunan University, Changsha, China
| | - Chunhua Wang
- College of Computer Science and Electronic Engineering, Hunan University, Changsha, China
| | - Quanli Deng
- College of Computer Science and Electronic Engineering, Hunan University, Changsha, China
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