Chaotic Dynamics in Neural Systems

Pusuluri, Krishna; Ju, Huiwen; Shilnikov, Andrey

doi:10.1007/978-1-0716-0421-2_738

Cited by 3 publications

(1 citation statement)

References 98 publications

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“…Recent studies have emphasized the exploration of chaotic and recurrent signals within neural networks [3][4][5]. Recurrence types, such as periodicity, quasi-periodicity, and Poisson stable motions, originate in the theory of celestial dynamics and have been applied to various areas of applied mathematics.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Symmetrical Discontinuous Hopfield Neural Networks with Poisson Stable Rates, Synaptic Connections and Unpredictable Inputs

Akhmet,

Nugayeva,

Seilova

2024

Symmetry

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The purpose of this paper is to study the dynamics of Hopfield neural networks with impulsive effects, focusing on Poisson stable rates, synaptic connections, and unpredictable external inputs. Through the symmetry of impulsive and differential compartments of the model, we follow and extend the principal dynamical ideas of the founder. Specifically, the research delves into the phenomena of unpredictability and Poisson stability, which have been examined in previous studies relating to models of continuous and discontinuous neural networks with constant components. We extend the analysis to discontinuous models characterized by variable impulsive actions and structural ingredients. The method of included intervals based on the B-topology is employed to investigate the networks. It is a novel approach that addresses the unique challenges posed by the sophisticated recurrence.

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Section: Introductionmentioning

confidence: 99%