Existence Canard Solutions For Four Dimensional Hindmarsh-Rose Model with Respect to Infinitesimal Parameter

Abstract

This research endeavor seeks to investigate the presence and viability of canard solutions within the context of the generalized Hindmarsh-Rose model, specifically when extended to four dimensions. To achieve this, nonstandard analysis is employed as a powerful tool for identifying and characterizing canard solutions within the four-dimensional singularly perturbed system, wherein two fast variables are considered in the folded saddle case. By undertaking this rigorous approach, we aim to contribute valuable insights to the understanding of canard phenomena in complex dynamical systems.

Keywords

• Singularly perturbed dynamical systems, Hindmarsh-Rose model, Canard solutions, Nonstandard analysis.