Synthesizing attractors of Hindmarsh-Rose neuronal systems

TL;DR

This paper introduces a parameter switching method to synthesize attractors in the Hindmarsh-Rose neuronal system, demonstrating that the synthesized attractor aligns with the averaged attractor and suggesting biological relevance.

Contribution

The paper presents a novel parameter switching scheme for attractor synthesis in neuronal models, expanding understanding of their dynamical behavior under parameter variations.

Findings

Synthesized attractors belong to the class of admissible attractors.

The synthesized attractor matches the averaged attractor from switched parameters.

The method demonstrates potential biological implications for neural adaptability.

Abstract

In this paper a periodic parameter switching scheme is applied to the Hindmarsh-Rose neuronal system to synthesize certain attractors. Results show numerically, via computer graphic simulations, that the obtained synthesized attractor belongs to the class of all admissible attractors for the Hindmarsh-Rose neuronal system and matches the averaged attractor obtained with the control parameter replaced with the averaged switched parameter values. This feature allows us to imagine that living beings are able to maintain vital behavior while the control parameter switches so that their dynamical behavior is suitable for the given environment.