Energy computation, infinitely coexisting patterns and their control from a Hindmarsh–Rose neuron with memristive autapse: Circuit implementation

Njitacke, Zeric Tabekoueng; Fozin, T. Fonzin; Muni, Sishu Shankar; Awrejcewicz, Jan; Kengne, Jacques

doi:10.1016/j.aeue.2022.154361

Cited by 27 publications

(10 citation statements)

References 43 publications

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“…Additionally, the frequency mismatch of the clock and the modulation signal causes an undesirable intermittency, as demonstrated in [39,40]. Te latter case is demonstrated in Figure 20 in the case of applying the control strategy (22).…”

Section: Possible Practical Implementation Of Multistability Controlmentioning

confidence: 91%

“…When the implementation is associated with the abrupt switching of the value of a, there can be a case when, after the control is disabled, the system is driven to an undesired mode (Figure 20(a)). Tat means, after the control is disabled, the trajectory occurs within the basin of attraction of (22): abrupt switching to and from the control strategy at t 1 and t 2 , respectively, (a) and with the further smooth attenuation of the control action from t 2 to t 3 (b).…”

Section: Possible Practical Implementation Of Multistability Controlmentioning

confidence: 99%

“…Particular cases of multistability are extreme multistability [21,22] characterized by an infnite number of coexisting attractors and megastability [23,24] producing an infnite number of nested attractors in a layered structure.…”

Section: Introductionmentioning

confidence: 99%

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Multistability and Its Control by the PWM Carrier Signal Modulation in a DC Electric Drive System

Kuznyetsov

2023

Mathematical Problems in Engineering

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Multistability is a universal nonlinear feature for many areas of physics and technology; for most applications, it is an undesired feature leading to uncertainty of the system’s functioning, and therefore, it should be controlled. We deal with the model of a multistable chopper-fed DC electric drive and study the control of multistability by the periodic modulation of a PWM (pulse-width modulation) carrier signal. The effect of utilizing sinusoidal modulation has been studied employing brute-force bifurcation diagrams as well as those obtained by numerical continuation, symbolic analysis of periodic modes, and normal form approximation of border-collision bifurcation. The result is formulated in terms of the acceptable amplitude of the modulation while the effect of phase shift is taken into account. As an alternative, a modified modulation in the form of the absolute value of the sine wave has been studied; the latter is characterized by a simpler bifurcation structure. Additionally, we propose an implementation of the adaptive control with the objective to drive the system away from a “nonnominal” mode. It has been demonstrated that such a transition should use smooth attenuation of the modulation signal to ensure the desired “nominal” operation of the system.

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Section: Possible Practical Implementation Of Multistability Controlmentioning

confidence: 91%

Section: Possible Practical Implementation Of Multistability Controlmentioning

confidence: 99%

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Multistability and Its Control by the PWM Carrier Signal Modulation in a DC Electric Drive System

Kuznyetsov

2023

Mathematical Problems in Engineering

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“…Discrete neuron models have advantages over continuous neuron models in terms of computational time, computational resources, and data storage. [37][38][39][40][41][42] Therefore, discrete neuron models are more suitable for simulating large-scale neu-ral networks and conducting general research, such as generating chaotic trajectories, pattern recognition, and analyzing synchronized firing behaviors. [43][44][45][46][47][48][49][50][51] As a result, research on discrete neurons has become a hot topic in recent years.…”

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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“…A recent review [11] gathers and discusses many neuron models from the perspective of dynamical systems theory. In continuous neuron systems [12,13], researchers found a variety of rich dynamics, computing energies associated with neurons, and infinite coexisting patterns in continuous time Hindmarsh-Rose systems. Recently, a physically reliable continuous Hindmarsh-Rose neuron model is studied [14].…”

Section: Introductionmentioning

confidence: 99%

Mode-locked orbits, doubling of invariant curves in discrete Hindmarsh-Rose neuron model

Muni

2023

Phys. Scr.

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Similar to period-doubling bifurcation of fixed points, periodic orbits, it has been found since 1980's that a corresponding doubling bifurcation can also be found in the case of quasiperiodic orbits. Doubling bifurcations of quasiperiodic orbits has an important consequence on the dynamics of the system under consideration. Recently, it has been shown that subsequent doublings of quasiperiodic closed invariant curves leads to the formation of Shilnikov attractors. In this contribution, we illustrate for the first time in a discrete neuron system, the phenomenon of doubling of closed invariant curves. We also show the presence of mode-locked orbits and the geometry of one-dimensional unstable manifolds associated to them resulting in the formation of a resonant closed invariant curve. Moreover, we illustrate the phenomenon of crisis, and multistability in the system.

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Energy computation, infinitely coexisting patterns and their control from a Hindmarsh–Rose neuron with memristive autapse: Circuit implementation

Cited by 27 publications

References 43 publications

Multistability and Its Control by the PWM Carrier Signal Modulation in a DC Electric Drive System

Multistability and Its Control by the PWM Carrier Signal Modulation in a DC Electric Drive System

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

Mode-locked orbits, doubling of invariant curves in discrete Hindmarsh-Rose neuron model

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