Coexisting attractors and multi-stability within a Lorenz model with periodic heating function

Abstract

In this paper, the classical Lorenz model is under investigation, in which a periodic heating term replaces the constant one. Applying the variable heating term causes time-dependent behaviors in the Lorenz model. The time series produced by this model are chaotic; however, they have fixed point or periodic-like qualities in some time intervals. The energy dissipation and equilibrium points are examined comprehensively. This modified Lorenz system can demonstrate multiple kinds of coexisting attractors by changing its initial conditions and, thus, is a multi-stable system. Because of multi-stability, the bifurcation diagrams are plotted with three different methods, and the dynamical analysis is completed by studying the Lyapunov exponents and Kaplan-Yorke dimension diagrams. Also, the attraction basin of the modified system is investigated, which approves the appearance of coexisting attractors in this system.