A Novel Megastable Oscillator with a Strange Structure of Coexisting Attractors: Design, Analysis, and FPGA Implementation

Abstract

Megastable chaotic systems are somehow the newest in the family of special chaotic systems. In this paper, a new megastable two-dimensional system is proposed. In this system, coexisting attractors are in some islands, interestingly covered by megalimit cycles. The introduced two-dimensional system has no defined equilibrium point. However, it seems that the origin plays the role of an unstable equilibrium point. Therefore, the attractors are determined as hidden attractors. Adding a forcing term to the system, we can obtain chaotic solutions and coexisting strange attractors. Moreover, the effect of three different values of the forcing term’s amplitude is studied. The dynamical properties of the designed system are investigated using attractor plots, bifurcation diagrams, and Lyapunov Exponents diagram. Phase portraits of the novel megastable oscillator are presented by FPGA design. Xilinx system generator block diagrams of the proposed system and trigonometric functions are also presented.

Local and Network Dynamics of a Non-Integer Order Resistor–Capacitor Shunted Josephson Junction Oscillators

“…Distinct colors represent different attractors for various initial conditions. We observed a few periodic attractors coexisting with chaotic attractors, while prior studies have shown that chaotic attractors can coexist with torus attractors alone [61,62]. As a result, the coexistence of periodic and chaotic attractors that we observed here is interesting and has yet to be reported in the literature.…”

Dynamical Analysis of a Quadratic Megastable Chaotic Oscillator and Its Application in Biometric Fingerprint Image Encryption

“…Te stability analysis [8] can be found using the Jacobian matrix and eigenvalues as given in equations ( 4) and (6).…”

“…Te countable number of infnite attractors which can generate for diferent initial conditions supports well for infnite number of key generations. Many works of literature recommended megastable oscillators for designing encryption algorithms, but to the best of our knowledge, most of them have an external excitation [6,7]. It motivates us towards developing a megastable oscillator without external excitation.…”

Chaotic Behaviors and Coexisting Attractors in a New Nonlinear Dissipative Parametric Chemical Oscillator

“…is is due to the fact that it provides multiple optional steady states for the system to respond to different needs. To that end, various studies on some driven nonlinear systems have shown the existence of multiple coexisting attractors [32][33][34][35][36][37][38][39]. In nonlinear chemical dynamics, the coexistence of two or more stable dynamical states (steady state, periodic oscillation, and chaos) of a system, under the same set of external constraints-input concentration of reactants, temperature, pressure, and so on, is one of the most interesting and significant phenomena.…”