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.

Generating rotationally hidden attractive sea via a new chaotic system with two mixed memristors

“…Recently, the research for the dynamic behavior of memristive chaotic system has become a hot issue [22]. In particular, several studies show that it can improve chaotic performance by introducing the memristive model to some chaotic systems [23][24][25][26][27][28]. Otherwise, the introduction of memristor can effectively improve the memory performance of neural network.…”

On two-parameter bifurcation and analog circuit implementation of a Chameleon chaotic system

“…For most autonomous ordinary differential equations (ODE) chaotic systems, the chaotic motions can be triggered by choosing an initial point in the small neighborhood of the systems' unstable equilibrium (if exists) since these motions are common self-excited oscillations [4][5][6]. The generated attractors in these systems usually have relatively large basins of attraction wrapping up at least one unstable equilibrium, such as the scroll-type Chua's attractor [7][8][9], the butterfly-type Lorenz attractor [10][11][12], and many other chaotic attractors in various nonlinear circuits and systems [13][14][15]. In recent decade, with the birth of the theory of hidden attractors and hidden oscillations [16][17][18], some relatively new hidden oscillating systems have attracted special interest [19][20][21].…”