Extreme multistability and phase synchronization in a heterogeneous bi-neuron Rulkov network with memristive electromagnetic induction

Xu, Quan; Liu, Tong; Ding, Shoukui; Bao, Han; Li, Ze; Chen, Bei

doi:10.1007/s11571-022-09866-3

Cited by 88 publications

(19 citation statements)

References 56 publications

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“…Due to their unique biomimetic properties, such as nanoscale size, low power consumption, and non-volatility, continuous memristors are considered the optimal choice for simulating synapses in analog form. [25][26][27][28][29][30] Compared to conventional electronic synapses, neural networks based on memristive synapses can more effectively mimic the complex firing activity of biological neural networks. For instance, memristor-coupled neural networks can generate grid multiscroll attractors, [31][32][33][34] diverse chaotic attractors that are employed in image encryption.…”

Section: Introductionmentioning

confidence: 99%

Dynamical behavior of memristor-coupled heterogeneous discrete neural networks with synaptic crosstalk

Ma 马,

Xiong 熊,

Li 李

et al. 2024

Chinese Phys. B

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Synaptic crosstalk is a prevalent phenomenon among neuronal synapses, playing a crucial role in the transmission of neural signals. Therefore, considering synaptic crosstalk behavior and investigating the dynamical behavior of discrete neural networks is highly necessary. In this paper, we propose a heterogeneous discrete neural network (HDNN) consisting of a three-dimensional KTz discrete neuron and a Chialvo discrete neuron. These two neurons are coupled mutually by two discrete memristors and the synaptic crosstalk is considered. The impact of crosstalk strength on the firing behavior of the HDNN is explored through bifurcation diagrams and Lyapunov exponents. It is observed that the HDNN exhibits different coexisting attractors under varying crosstalk strengths. Furthermore, the influence of different crosstalk strengths on the synchronized firing of the HDNN is investigated, revealing a gradual attainment of phase synchronization between the two discrete neurons as the crosstalk strength decreases.

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Section: Introductionmentioning

confidence: 99%

Dynamical behavior of memristor-coupled heterogeneous discrete neural networks with synaptic crosstalk

Ma 马,

Xiong 熊,

Li 李

et al. 2024

Chinese Phys. B

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“…A two-neuron network is established by coupling two Morris-Lecar neurons using a memristor synapse and shown to devellop chaotic behaviors [22]. Xu et al proposed a coupled Rulkov bi-neuron system and investigate the memristive electromagnetic effects [23]. The coupled model reveals chaos, and infinitely multiple firing partners.…”

Section: Introductionmentioning

confidence: 99%

Collective dynamics of two coupled Hopfield inertial neurons with different activation functions: theoretical study and microcontroller implementation

Madasamy,

Boui a Boya,

Kengne

et al. 2023

Phys. Scr.

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This work deals with the regular and chaotic dynamics of a system made up of two Hopfield-type neurons with two different activation functions: the hyperbolic tangent function and the Crespi function. The mathematical model is in the form of an autonomous differential system of order four with odd symmetry. The analysis highlights nine equilibrium points and four of these points experience a Hopf bifurcation at the same critical value of a control parameter which can be either the diss1ipation parameter or one of the coupling coefficients. This makes plausible the presence of four parallel bifurcation branches as well as the coexistence of multiple attractors in the behavior of the system. One of the highlights revealed in this work is the coexistence of three double-scroll type attractors of particular topology as well as the presence of a four-spiral attractor. Furthermore, the coexistence of both self-excited and hidden dynamics is also reported. All this plethora of dynamics is elucidated by making use of the usual tools for analyzing nonlinear systems such as bifurcation diagrams, the maximum of Lyapunov exponent, basins of attractions as well as phase portraits. A physical implementation of the microcontroller-based system is envisaged in order to confirm the plethora of behaviors observed theoretically.

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“…Thus, modeling of the biological neuron and exploring its dynamical behaviors are research hotspots and attract many researchers' attention. Up to date, numerous neuron models have been constructed to depict different OPEN ACCESS EDITED BY kinds of biological neurons, and they can roughly be divided into two categories, i.e., the continuous-time neuron model [4][5][6][7][8][9][10] and discrete-time map [11][12][13]. In the literature, some of the continuous-time neuron models were built based on the electrophysiological ion transport mechanism [4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Hidden firing patterns and memristor initial condition-offset boosting behavior in a memristive Hindmarsh-Rose neuron model

et al. 2023

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Electromagnetic induction can effectively induce abundant firing patterns in neurons. In modeling a neuron model with the electromagnetic induction effect, an electromagnetic induction current is frequently added to the state equation of membrane potential. To more properly reflect the non-uniform distribution of the ions inside and outside the neuron membrane, an ideal flux-controlled memristor with sinusoidal memductance function and non-linearly modulated input is raised to depict an electromagnetic induction effect on a Hindmarsh–Rose neuron model, and thereby, a three-dimensional (3D) memristive Hindmarsh–Rose (mHR) neuron model is built in this paper. The proposed mHR neuron model possesses no equilibrium point since the involvement of the ideal flux-controlled memristor, which induces the generation of hidden dynamics. Numerical results declare that the mHR neuron model can generate abundant hidden dynamics, i.e., periodic spiking, chaotic spiking, period-doubling bifurcation route, tangent bifurcation, and chaos crisis. These hidden dynamics are much related to the memristor coupling strength and externally applied stimulus. Afterward, the memristor initial condition-offset boosting behavior is revealed. This can trigger the generation of infinite multiple coexisting firing patterns along the memristor variable coordinate. These coexisting firing patterns have identical attractor topology but different locations in the phase plane. Finally, an analog circuit is designed for implementing the mHR neuron model, and PSIM-based circuit simulation is executed. The circuit-simulated results perfectly verify the generation of hidden infinite multiple coexisting initial condition-offset boosting firing patterns in the proposed mHR neuron model.

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Extreme multistability and phase synchronization in a heterogeneous bi-neuron Rulkov network with memristive electromagnetic induction

Cited by 88 publications

References 56 publications

Dynamical behavior of memristor-coupled heterogeneous discrete neural networks with synaptic crosstalk

Dynamical behavior of memristor-coupled heterogeneous discrete neural networks with synaptic crosstalk

Collective dynamics of two coupled Hopfield inertial neurons with different activation functions: theoretical study and microcontroller implementation

Hidden firing patterns and memristor initial condition-offset boosting behavior in a memristive Hindmarsh-Rose neuron model

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