A New Memristive Neuron Map Model and Its Network’s Dynamics under Electrochemical Coupling

Ramakrishnan, Balamurali; Mehrabbeik, Mahtab; Parastesh, Fatemeh; Rajagopal, Karthikeyan; Jafari, Sajad

doi:10.3390/electronics11010153

Cited by 46 publications

(9 citation statements)

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“…In the membrane potential u i -equations, the nonlinear term k tanh(ρ i )u i presents the memristive coupling effect [24,33,36], where ρ i (t, x) stands for the memductance of the memristor and tanh(ρ i ) is the the electromagnetic induction flux with its coupling strength coefficient k. In this system, the fast excitatory variable u i (t, x) refers to the transmembrane electrical potential of a neuron cell and the slow recovering variable w i (t, x) represents the integrated ionic current across the neuron membrane. The network neuron coupling terms are assumed to be linear with a common strength coefficient P in the membrane potential equation.…”

Section: Introductionmentioning

confidence: 99%

“…The researches on memristive FitzHugh-Nagumo and Hindmarsh-Rose neural networks in ordinary differential equations have been expanding in the recent decade, cf. [1,8,16,24,40] and many references therein. Various synchronization results with memristive effect of these models are achieved [10,13,19,22,31,32,35] mainly by the methods of generalized Hamiltonian functions, Lyapunov exponents, and the computational algebra with numerical simulations.…”

Section: Introductionmentioning

confidence: 99%

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Synchronization of Memristive FitzHugh-Nagumo Neural Networks

You¹,

Tian²,

Tu³

2023

Preprint

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A new mathematical model of neural networks described by diffusive FitzHugh-Nagumo equations with memristors and linear synaptic coupling is proposed and investigated. The existence of absorbing set for the solution semiflow in the energy space is proved and global dynamics of the memristive neural networks are dissipative. Through uniform estimates and maneuver of integral inequalities on the interneuron difference equations, it is shown that exponential synchronization of the neural network at a uniform convergence rate occurs if the coupling strength satisfies a threshold condition explicitly expressed by the system parameters, which is illustrated by an example and numerical simulation experiments.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Synchronization of Memristive FitzHugh-Nagumo Neural Networks

You¹,

Tian²,

Tu³

2023

Preprint

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“…[3] Very recently, discrete memristor has begun to receive many researchers' attention. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] For instance, Peng et al presented a model of discrete memristor via the difference theory and derived a memristive Hénon map in Ref. [4].…”

Section: Introductionmentioning

confidence: 99%

Extremely hidden multi-stability in a class of two-dimensional maps with a cosine memristor

et al. 2022

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In this work, we present a class of two-dimensional memristive maps with a cosine memristor. The memristive maps do not have any fixed points, so they belong to the category of nonlinear maps with hidden attractors. The rich dynamical behaviors of these maps are demonstrated and investigated using different numerical tools, including phase portrait, basins of attraction, bifurcation diagram, and Lyapunov exponents. The two-parameter bifurcation analysis of the memristive map has been carried out to reveal the bifurcation mechanism of the dynamical behaviors. Based on our extensive simulation studies, the proposed memristive maps can produce hidden periodic, chaotic, and hyper-chaotic attractors. They can exhibit extremely hidden multi-stability, namely the coexistence of infinite hidden attractors, rarely shown in memristive maps. Potentially, this work can be used for secure communication, such as data and image encryption.

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“…Recently, investigating the synchronization state in the coupled oscillators has aroused much interest and drew attention [19,20]. Complete synchronization refers to the state in which all oscillators temporally behave in a simultaneous way [21]. Synchronization, especially complete synchronization [22], phase synchronization [23], and chimera [24], which is the coexistence of synchronized and asynchronized states [25], is a phenomenon that is observed in the real world, such as in biology [26] and climate [27].…”

mentioning

confidence: 99%

Synchronization and different patterns in a network of diffusively coupled elegant Wang–Zhang–Bao circuits

Ramakrishnan

Falah

et al. 2022

Eur. Phys. J. Spec. Top.

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Synchronization in coupled oscillators is of high importance in secure communication and information processing. Due to this reason, a significant number of studies have been performed to investigate the synchronization state in coupled circuits. Diffusive coupling is the simplest connection between the oscillators, which can be implemented through a variable resistor between two variables of two circuits. The Chua's circuit is the most famous chaotic circuit whose dynamics have been investigated in many studies. However, Wang-Zhang-Bao (WZB) is another chaotic circuit that can exhibit exciting behaviors such as bistability. Thus, this study aims to investigate the cooperative dynamics of the WZB circuit in its elegant parameter values. To this issue, first, we explored the dynamic behavior of the elegant WZB circuit using the bifurcation diagrams, the Lyapunov exponents, and the basins of attraction. Based on the results, we found the range of the bifurcation parameter and the initial conditions wherein the system is bistable. Subsequently, setting the parameters in the monostable region, we studied the synchronization state of two diffusively coupled WZB circuits analytically and numerically. Consequently, we used master stability functions and temporally averaged synchronization error as the analytical and numerical tools to explore the synchronization state. Then we numerically examined the synchronization state in a network of 100 nonlocally coupled WZB oscillators. As a result, we found imperfect chimera and phase synchronization in the studied network before getting synchronized.

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A New Memristive Neuron Map Model and Its Network’s Dynamics under Electrochemical Coupling

Cited by 46 publications

References 46 publications

Synchronization of Memristive FitzHugh-Nagumo Neural Networks

Synchronization of Memristive FitzHugh-Nagumo Neural Networks

Extremely hidden multi-stability in a class of two-dimensional maps with a cosine memristor

Synchronization and different patterns in a network of diffusively coupled elegant Wang–Zhang–Bao circuits

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