A New Megastable Oscillator with Rational and Irrational Parameters

Abstract

In this paper, a new two-dimensional nonlinear oscillator with an unusual sequence of rational and irrational parameters is introduced. This oscillator has endless coexisting limit cycles, which make it a megastable dynamical system. By periodically forcing this system, a new system is designed which is capable of exhibiting an infinite number of coexisting asymmetric torus and strange attractors. This system is implemented by an analog circuit, and its Hamiltonian energy is calculated.

Dynamic Analysis and Degenerate Hopf Bifurcation‐Based Feedback Control of a Conservative Chaotic System and Its Circuit Simulation

“…In 2011, Leonov first discovered the hidden attractors in Chua's chaotic circuit [8]; unlike the Shilnikov-type attractors, these hidden attractors are with a basin of attraction which does not contain neighborhoods of equilibria and cannot be determinated by the Shilnikov condition. In the last decade, the systems with hidden attractors mainly include chaotic systems without equilibrium [9], with infinite equilibrium [10,11], and with only one stable equilibrium [12][13][14][15][16][17]. Although many chaotic systems with hidden attractors have been proposed, most of them are mainly studied by numerical simulation, and the main dynamic behaviors studies are focused on the local structures, while the studies on the global dynamics are relatively rare; hence, it is necessary to study the global dynamics and bifurcation of chaotic systems with hidden attractors to reveal the mechanism of chaos.…”

Special chaotic systems

“…Such a system is called "multi-stable" [17,18]. A system that has a countable infinity of coexisting attractors a e-mail: sajadjafari83@gmail.com is called "megastable" [19][20][21][22], while a system with an uncountable infinity of coexisting attractors is called "extreme multi-stable" [23][24][25]. Chaotic systems with different multi-stabilities can satisfy the novelty conditions of the standard for proposing chaotic systems.…”