A family of coexisting multi-scroll chaos and its selected control in coupled non-oscillatory neurons: A case study

Abstract

This study presents a family of coexisting multi-scroll chaos in a network of coupled non-oscillatory neurons. The dynamics of the system are analyzed using phase portraits, basins of attraction, time series, bifurcation diagrams, and spectra of Lyapunov exponents. The coexistence of multiple bifurcation diagrams leads to a complex pattern of multi-scroll formation, which is further complicated by the presence of coexisting single-scroll attractors that merge to form multi-scroll chaos. In addition, the presence of bursting phenomena and multiple firing partners is present in the model. A control strategy based on a noninvasive control method is applied to select the desired multi-scroll. The effectiveness of the control method is demonstrated through numerical simulations. The experimental validation on an Arduino microcontroller confirms the theoretical results and demonstrates the feasibility of implementing the proposed model. These remarkable behaviors hold significant implications for understanding brain dynamics and have potential applications in various fields.

Keywords

• Hopfield inertial neurons
• Coexisting multi-scroll chaos
• Basins of attraction
• Bursting oscillation
• and multistability control