• A generalized scheme for designing multistable continuous dynamical systems

• # Fulltext

https://www.ias.ac.in/article/fulltext/pram/086/06/1183-1193

• # Keywords

Multistability; bifurcation; Lyapunov exponent; synchronization.

• # Abstract

In this paper, a generalized scheme is proposed for designing multistable continuous dynamical systems. The scheme is based on the concept of partial synchronization of states and the concept of constants of motion. The most important observation is that by coupling two mdimensional dynamical systems, multistable nature can be obtained if i number of variables of the two systems are completely synchronized and j number of variables keep a constant difference between them i.e., their differences are constants of motion, where $i+j = m$ and $1 \le i, j \le m−1$. The proposed scheme is illustrated by taking coupled Lorenz systems and coupled chaotic Lorenzlike systems. According to the scheme, two coupled systems reduce to single modified system withsome initial condition-dependent parameters. Time evolution plots, phase diagrams, variation of maximum Lyapunov exponent and bifurcation diagrams of the systems are presented to show the multistable nature of the coupled systems.

• # Author Affiliations

1. Department of Applied Mathematics, University of Calcutta, Kolkata 700 009, India

• # Pramana – Journal of Physics

Volume 94, 2020
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Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019