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Rajagopal K, Karthikeyan A. Complex dynamics in a fractional order nephron pressure and flow regulation model. Biosystems 2023:104931. [PMID: 37330035 DOI: 10.1016/j.biosystems.2023.104931] [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: 08/27/2022] [Revised: 05/11/2023] [Accepted: 05/11/2023] [Indexed: 06/19/2023]
Abstract
Cardiovascular diseases can be attributed to irregular blood pressure, which may be caused by malfunctioning kidneys that regulate blood pressure. Research has identified complex oscillations in the mechanisms used by the kidney to regulate blood pressure. This study uses established physiological knowledge and earlier autoregulation models to derive a fractional order nephron autoregulation model. The dynamical behaviour of the model is analyzed using bifurcation plots, revealing periodic oscillations, chaotic regions, and multistability. A lattice array of the model is used to study collective behaviour and demonstrates the presence of chimeras in the network. A ring network of the fractional order model is also considered, and a diffusion coupling strength is adopted. A basin of synchronization is derived, considering coupling strength, fractional order or number of neighbours as parameters, and measuring the strength of incoherence. Overall, the study provides valuable insights into the complex dynamics of the nephron autoregulation model and its potential implications for cardiovascular diseases.
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Affiliation(s)
| | - Anitha Karthikeyan
- Department of Electronics and Communications Engineering and University Centre for Research & Development, Chandigarh University, Mohali, 140413, Punjab, India; Department of Electronics and Communications Engineering, Vemu Institute of Technology, India.
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He S, Rajagopal K, Karthikeyan A, Srinivasan A. A discrete Huber-Braun neuron model: from nodal properties to network performance. Cogn Neurodyn 2023; 17:301-310. [PMID: 36704635 PMCID: PMC9871134 DOI: 10.1007/s11571-022-09806-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2021] [Revised: 03/15/2022] [Accepted: 03/30/2022] [Indexed: 01/29/2023] Open
Abstract
Many of the well-known neuron models are continuous time systems with complex mathematical definitions. Literatures have shown that a discrete mathematical model can effectively replicate the complete dynamical behaviour of a neuron with much reduced complexity. Hence, we propose a new discrete neuron model derived from the Huber-Braun neuron with two additional slow and subthreshold currents alongside the ion channel currents. We have also introduced temperature dependent ion channels to study its effects on the firing pattern of the neuron. With bifurcation and Lyapunov exponents we showed the chaotic and periodic regions of the discrete model. Further to study the complexity of the neuron model, we have used the sample entropy algorithm. Though the individual neuron analysis gives us an idea about the dynamical properties, it's the collective behaviour which decides the overall behavioural pattern of the neuron. Hence, we investigate the spatiotemporal behaviour of the discrete neuron model in single- and two-layer network. We have considered obstacle as an important factor which changes the excitability of the neurons in the network. Literatures have shown that spiral waves can play a positive role in breaking through quiescent areas of the brain as a pacemaker by creating a coherence resonance behaviour. Hence, we are interested in studying the induced spiral waves in the network. In this condition when an obstacle is introduced the wave propagation is disturbed and we could see multiple wave re-entry and spiral waves. In a two-layer network when the obstacle is considered only in one layer and stimulus applied to the layer having the obstacle, the wave re-entry is seen in both the layer though the other layer is not exposed to obstacle. But when both the layers are inserted with an obstacle and stimuli also applied to the layers, they behave like independent layers with no coupling effect. In a two-layer network, stimulus play an important role in spatiotemporal dynamics of the network. Supplementary Information The online version contains supplementary material available at 10.1007/s11571-022-09806-1.
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Affiliation(s)
- Shaobo He
- School of Physics and Electronics, Central South University, Changsha, 410083 China
| | | | - Anitha Karthikeyan
- Department of Electronics and Communication Engineering, Prathyusha Engineering College, Chennai, India
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Rajagopal K, He S, Duraisamy P, Karthikeyan A. Spiral waves in a hybrid discrete excitable media with electromagnetic flux coupling. CHAOS (WOODBURY, N.Y.) 2021; 31:113132. [PMID: 34881596 DOI: 10.1063/5.0066157] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2021] [Accepted: 10/27/2021] [Indexed: 06/13/2023]
Abstract
Though there are many neuron models based on differential equations, the complexity in realizing them into digital circuits is still a challenge. Hence, many new discrete neuron models have been recently proposed, which can be easily implemented in digital circuits. We consider the well-known FitzHugh-Nagumo model and derive the discrete version of the model considering the sigmoid type of recovery variable and electromagnetic flux coupling. We show the various time series plots confirming the existence of periodic and chaotic bursting as in differential equation type neuron models. Also, we have used the bifurcation plots, Lyapunov exponents, and frequency bifurcations to investigate the dynamics of the proposed discrete neuron model. Different topologies of networks like single, two, and three layers are considered to analyze the wave propagation phenomenon in the network. We introduce the concept of using energy levels of nodes to study the spiral wave existence and compare them with the spatiotemporal snapshots. Interestingly, the energy plots clearly show that when the energy level of nodes is different and distributed, the occurrence of the spiral waves is identified in the network.
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Affiliation(s)
- Karthikeyan Rajagopal
- Center for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India
| | - Shaobo He
- School of Physics and Electronics, Central South University, Changsha 410083, China
| | - Prakash Duraisamy
- Center for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India
| | - Anitha Karthikeyan
- Department of Electronics and Communication Engineering, Prathyusha Engineering College, Chennai 602025, India
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Ding D, Jiang L, Hu Y, Yang Z, Li Q, Zhang Z, Wu Q. Hidden coexisting firings in fractional-order hyperchaotic memristor-coupled HR neural network with two heterogeneous neurons and its applications. CHAOS (WOODBURY, N.Y.) 2021; 31:083107. [PMID: 34470251 DOI: 10.1063/5.0053929] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2021] [Accepted: 07/09/2021] [Indexed: 06/13/2023]
Abstract
The firing patterns of each bursting neuron are different because of the heterogeneity, which may be derived from the different parameters or external drives of the same kind of neurons, or even neurons with different functions. In this paper, the different electromagnetic effects produced by two fractional-order memristive (FOM) Hindmarsh-Rose (HR) neuron models are selected for characterizing different firing patterns of heterogeneous neurons. Meanwhile, a fractional-order memristor-coupled heterogeneous memristive HR neural network is constructed via coupling these two heterogeneous FOM HR neuron models, which has not been reported in the adjacent neuron models with memristor coupling. With the study of initial-depending bifurcation behaviors of the system, it is found that the system exhibits abundant hidden firing patterns, such as periods with different topologies, quasiperiodic firings, chaos with different topologies, and even hyperchaotic firings. Particularly, the hidden hyperchaotic firings are perfectly detected by two-dimensional Lyapunov stability graphs in the two-parameter space. Meanwhile, the hidden coexisting firing patterns of the system are excited from two scattered attraction domains, which can be confirmed from the local attraction basins. Furthermore, the color image encryption based on the system and the DNA approach owns great keyspace and a good encryption effect. Finally, the digital implementations based on Advanced RISC Machine are in good coincidence with numerical simulations.
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Affiliation(s)
- Dawei Ding
- School of Electronics and Information Engineering, Anhui University, Hefei 230601, China
| | - Li Jiang
- School of Electronics and Information Engineering, Anhui University, Hefei 230601, China
| | - Yongbing Hu
- School of Electronics and Information Engineering, Anhui University, Hefei 230601, China
| | - Zongli Yang
- School of Electronics and Information Engineering, Anhui University, Hefei 230601, China
| | - Qian Li
- School of Electronics and Information Engineering, Anhui University, Hefei 230601, China
| | - Zhixin Zhang
- School of Mathematics Sciences, Anhui University, Hefei 230601, China
| | - Qiujie Wu
- School of Internet, Anhui University, Hefei 230601, China
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Rajagopal K, Jafari S, Karthikeyan A, Srinivasan A. Effect of magnetic induction on the synchronizability of coupled neuron network. CHAOS (WOODBURY, N.Y.) 2021; 31:083115. [PMID: 34470222 DOI: 10.1063/5.0061406] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2021] [Accepted: 07/28/2021] [Indexed: 06/13/2023]
Abstract
Master stability functions (MSFs) are significant tools to identify the synchronizability of nonlinear dynamical systems. For a network of coupled oscillators to be synchronized, the corresponding MSF should be negative. The study of MSF will normally be discussed considering the coupling factor as a control variable. In our study, we considered various neuron models with electromagnetic flux induction and investigated the MSF's zero-crossing points for various values of the flux coupling coefficient. Our numerical analysis has shown that in all the neuron models we considered, flux coupling has increased the synchronization of the coupled neuron by increasing the number of zero-crossing points of MSFs or by achieving a zero-crossing point for a lesser value of a coupling parameter.
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Affiliation(s)
- Karthikeyan Rajagopal
- Center for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, Tamil Nadu, India
| | - Sajad Jafari
- Biomedical Engineering Department, Amirkabir University of Technology, Tehran 1591634311, Iran
| | - Anitha Karthikeyan
- Department of Electronics and Communication Engineering, Prathyusha Engineering College, Thiruvallur, Tamil Nadu 602025, India
| | - Ashokkumar Srinivasan
- Center for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, Tamil Nadu, India
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Rajagopal K, Jafari S, Moroz I, Karthikeyan A, Srinivasan A. Noise induced suppression of spiral waves in a hybrid FitzHugh-Nagumo neuron with discontinuous resetting. CHAOS (WOODBURY, N.Y.) 2021; 31:073117. [PMID: 34340329 DOI: 10.1063/5.0059175] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2021] [Accepted: 06/22/2021] [Indexed: 06/13/2023]
Abstract
A modified FitzHugh-Nagumo neuron model with sigmoid function-based recovery variable is considered with electromagnetic flux coupling. The dynamical properties of the proposed neuron model are investigated, and as the excitation current becomes larger, the number of fixed points decreases to one. The bifurcation plots are investigated to show the chaotic and periodic regimes for various values of excitation current and parameters. A N×N network of the neuron model is constructed to study the wave propagation and wave re-entry phenomena. Investigations are conducted to show that for larger flux coupling values, the spiral waves are suppressed, but for such values of the flux coupling, the individual nodes are driven into periodic regimes. By introducing Gaussian noise as an additional current term, we showed that when noise is introduced for the entire simulation time, the dynamics of the nodes are largely altered while the noise exposure for 200-time units will not alter the dynamics of the nodes completely.
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Affiliation(s)
- Karthikeyan Rajagopal
- Center for Nonlinear Systems, Chennai Institute of Technology, Chennai, Tamil Nadu 600069, India
| | - Sajad Jafari
- Department of Biomedical Engineering, Amirkabir University of Technology, Tehran 1591634311, Iran
| | - Irene Moroz
- Mathematical Institute, University of Oxford, Andrew Wiles Building, Oxford OX1 2JD, United Kingdom
| | - Anitha Karthikeyan
- Department of Electronics and Communication Engineering, Prathyusha Engineering College, Tiruvallur, Tamil Nadu 602025, India
| | - Ashokkumar Srinivasan
- Center for Nonlinear Systems, Chennai Institute of Technology, Chennai, Tamil Nadu 600069, India
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Tan Y, Wang C. A simple locally active memristor and its application in HR neurons. CHAOS (WOODBURY, N.Y.) 2020; 30:053118. [PMID: 32491896 DOI: 10.1063/1.5143071] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2019] [Accepted: 04/22/2020] [Indexed: 06/11/2023]
Abstract
This paper proposes a simple locally active memristor whose state equation only consists of linear terms and an easily implementable function and design for its circuit emulator. The effectiveness of the circuit emulator is validated using breadboard experiments and numerical simulations. The proposed circuit emulator has a simple structure, which not only reduces costs but also increases its application value. The power-off plot and DC V-I Loci verify that the memristor is nonvolatile and locally active, respectively. This locally active memristor exhibits low cost, easy physical implementation, and wide locally active region characteristics. Furthermore, a neural model composed of two 2D HR neurons based on the proposed locally active memristor is established. It is found that complicated firing behaviors occur only within the locally active region. A new phenomenon is also discovered that shows coexisting position symmetry for different attractors. The firing pattern transition is then observed via bifurcation analysis. The results of MATLAB simulations are verified from the hardware circuits.
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Affiliation(s)
- Yumei Tan
- College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China
| | - Chunhua Wang
- College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China
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