A new 3-D chaotic system with a curve equilibrium: Bifurcation analysis, multistability, circuit design and~complete synchronization design

Abstract

In this study, a new three-dimensional chaotic system has been derived by adding two nonlinearities to Sambas chaotic system (2019) with a curve equilibrium. It is shown that the new chaotic system also features the same curve equilibrium as the Sambas chaotic system (2019), namely a pair of circles in the (x, y)-plane with centers in the x-axis and intersecting at the origin. It is established that the new chaotic system with a curve equilibrium has more complexity than the Sambas chaotic system (2019) with a curve equilibrium. Next, a detailed bifurcation analysis is presented for the new chaotic system with a curve equilibrium. Multistability analysis for the new chaotic system with a curve equilibrium is exhibited by the coexistence of two chaotic attractors for the same parameters as in the chaotic case but different values of the initial states. Using Multisim, an electronic circuit design for the proposed chaotic system has been exhibited which will be useful for practical implementations. Using integral sliding mode control (ISMC), complete synchronization of a pair of new chaotic systems taken as the master and slave systems has been achieved. Simulations using MATALB R2024b have been shown to illustrate the main results of this paper.  The proposed chaotic system with a curve equilibrium will be useful for applications in science and engineering.