Hamilton energy, complex dynamical analysis and information patterns of a new memristive FitzHugh-Nagumo neural network

Njitacke, Zeric Tabekoueng; Takembo, Clovis Ntahkie; Awrejcewicz, Jan; Fouda, H. P. Ekobena; Kengne, Jacques

doi:10.1016/j.chaos.2022.112211

Cited by 40 publications

(9 citation statements)

References 44 publications

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“…All biological and physical systems posses their own internal energy which are associated to their state variables and parameters [37,38,25,39]. This section is devoted to the computation of the Hamiltonian energy of system (11) derived from the Helmholtz theorem [37,38,40]. From that equation, effects of offset boosting parameter m could also be investigated.…”

Section: Hamilton Energy Computationmentioning

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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Section: Hamilton Energy Computationmentioning

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 behavior of both single and a network of FHN neuron with memristors were investigated in ref. [46]. The investigation of the single neuron revealed the presence of hidden dynamics, which is an interesting feature in the qualitative theory of dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

Route to Chaos and Chimera States in a Network of Memristive Hindmarsh-Rose Neurons Model with External Excitation

Muni

Njitacke

Feudjio

et al. 2022

Chaos Theory and Applications

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In this paper we have introduced and investigated the collective behavior of a network of memristive Hindmarsh-Rose (HR) neurons. The proposed model was built considering the memristive autapse of the traditional 2D HR neuron. Using the one-parameter bifurcation diagram and its corresponding maximal Lyapunov exponent graph, we showed that the proposed model was able to exhibit a reverse period doubling route to chaos, phenomenon of interior and exterior crises. Three different configurations of the ring-star network of the memristive HR neuron model, including ring-star, ring, and star, have been considered. The study of those network configurations revealed incoherent, coherent , chimera and cluster state behaviors. Coherent behavior is characterized by synchronization of the neurons of the network, while incoherent behaviors are characterized by the absence of synchronization. Chimera states refer to a differet state where there is a coexistence of synchroniaed and asynchronized nodes of the network. One of the interesting result of the paper is the prevalence of double-well chimera states in both ring and ring-star network and has been first mentioned in the case of memrisitve HR neuron model.

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“…Note that the analysis of coupled neurons using both memristive autapse and memristive synapse has not yet been reported. Tabekoueng and colleagues used a memristive synapse to connect a FitzHugh-Nagumo (2D) neuron to a Hindmarsh-Rose (3D) neuron [12]. The dynamics reveals the coexistence of infinite patterns in the state space [13].…”

Section: Introductionmentioning

confidence: 99%

A memristive autapse-synapse neural network: application to image encryption

Zhang¹,

Jiang²,

Nkapkop³

et al. 2023

Phys. Scr.

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With the advent of the physical memristor, various memristive neural network models have been designed and analyzed to mimic some human brain functions. However, there is a realistic issue because many works reported the coupling of neuron models using either memristive synapse or memristive autapse, whereas in the real brain, a neuron can interact with both another neuron (memristive synapse) and with itself (memristive autapse). Two main ideas are developed in this work. First, we investigate the dynamics of two different neurons coupled via memristive synapse and memristive autapse. The analyses indicate that the global dynamics of this highly relies on the neuron's coupling strength. Second, a cryptographic scheme based on both S-box driven block compressive sensing and the memristive autapse synapse model is proposed. Performance analyses indicate that the coupling strength of the proposed neural network model can be adjusted to increase or decrease the security of medical data.

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Hamilton energy, complex dynamical analysis and information patterns of a new memristive FitzHugh-Nagumo neural network

Cited by 40 publications

References 44 publications

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

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

Route to Chaos and Chimera States in a Network of Memristive Hindmarsh-Rose Neurons Model with External Excitation

A memristive autapse-synapse neural network: application to image encryption

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