Complex Dynamics of Coupled Neurons Through a Memristive Synapse: Extreme Multistability and Its Control With Selection of the Desired State

Njitacke, Zeric Tabekoueng; Awrejcewicz, Jan; Telem, Adélaïde Nicole Kengnou; Fozin, T. Fonzin; Kengne, Jacques

doi:10.1109/tcsii.2022.3172141

Cited by 15 publications

(6 citation statements)

References 24 publications

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“…Hence, the necessity to design a control will enable us to move periodic states and maintain the chaotic state. Recently, By using the temporal feedback method introduced in [32] , Z. Njitacke and collaborators explored it to control any desired state without any modification of the topological structure of the attractors associated with that state. Wherever, this method is limited when the model present only coexistence of periodic state.…”

Section: Control Of Multistabilitymentioning

confidence: 99%

Four-scroll attractor on the dynamics of a novel Hopfield neural network based on bi-neurons without bias current

Boya¹,

Kengne²,

Kenmoé³

et al. 2022

Heliyon

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Section: Control Of Multistabilitymentioning

confidence: 99%

Four-scroll attractor on the dynamics of a novel Hopfield neural network based on bi-neurons without bias current

Boya¹,

Kengne²,

Kenmoé³

et al. 2022

Heliyon

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“…In the same line and, after all verifications, the Hamilton energy function for the nonlinearity min . The state variables of the system x(t), y(t) evolves with time and initial conditions in any one of the piecewiselinear region and the next region of operation depends on the existence of the state variable x as given by equation (23). The chaotic attractor of the system with the absolute nonlinearity in the x − y plane generated from the analytical solutions is as shown in figure 23(a)(ii).…”

Section: G(x)mentioning

confidence: 99%

“…The present work is focused on designing a class of second-order circuit systems with Sprott type simple nonlinear elements that exhibit chaos. Multistability is a situation in which a nonlinear system display several coexisting states for fixed set of system parameters but starting from different initial conditions [22,23]. Since its discovery by Arecchi et al [24], it has been reported in several biological [25], mechanical [26] and electronic [27] systems.…”

Section: Introductionmentioning

confidence: 99%

Energy computation and multistability in a class of second-order chaotic systems with simple nonlinearities: numerical, experimental and analytical results

Sivaganesh¹,

Srinivasan²,

Fozin³

et al. 2022

Phys. Scr.

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The present work is aimed at the design, implementation and analysis of generic new second-order non-autonomous chaotic systems with simple nonlinear functions that have algebraically simple representations in mathematical form. These systems involve simple second-order non-autonomous ordinary differential equations with different simple nonlinearities like $G(x) (= x^2, |x|, max(x)$ and $min(x))$. The present study deals with numerical simulation, experimental analog circuit simulation results to demonstrate the ordered and chaotic phenomena being exhibited by these systems. Of most interest the striking phenomenon of multistability is uncovered for certain nonlinearities. Coexisting attractors are harnessed through the offset boosting approach. Also, the Hamilton energy is established through the Helmholtz theorem. It is found that both methods can be exploited as a non-bifurcation approach in characterizing multistability in the model. Further, analytical solutions developed for systems with certain nonlinearities are presented and the chaotic behavior of the systems studied using the solutions validating the numerical and experimental results are reported.

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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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Complex Dynamics of Coupled Neurons Through a Memristive Synapse: Extreme Multistability and Its Control With Selection of the Desired State

Cited by 15 publications

References 24 publications

Four-scroll attractor on the dynamics of a novel Hopfield neural network based on bi-neurons without bias current

Four-scroll attractor on the dynamics of a novel Hopfield neural network based on bi-neurons without bias current

Energy computation and multistability in a class of second-order chaotic systems with simple nonlinearities: numerical, experimental and analytical results

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

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