Localization of Hidden Attractors in Chua’s System With Absolute Nonlinearity and Its FPGA Implementation

Investigation of the classical self-excited and hidden attractors in the modified Chua’s circuit is a hot and interesting topic. In this article, a novel Chua’s circuit system with an absolute item is investigated. According to the mathematical model, dynamic characteristics are analyzed, including symmetry, equilibrium stability analysis, Hopf bifurcation analysis, Lyapunov exponents, bifurcation diagram, and the basin of attraction. The hidden attractors are located theoretically. Then, the coexistence of the hidden limit cycle and self-excited chaotic attractors are observed numerically and experimentally. The numerical simulation results are consistent with the FPGA implementation results. It shows that the hidden attractor can be localized in the digital circuit.

Controlling Chaotic Systems via Time-delayed Control

Based on Lyapunov stabilization theory, this paper proposes a proportional plus integral time-delayed controller to stabilize unstable equilibrium points (UPOs) embedded in chaotic attractors. The criterion is successfully applied to the classic Chua's circuit. Theoretical analysis and numerical simulation show the effectiveness of this controller.

Chua’s Circuit Simulation Experiment Based on Saturation Function

This paper designs a Chua's diode circuit based on saturation function. It uses Matlab/Simulink to model Chua's circuit, and simulates and analyzes the dynamic behavior of chaos, the model simply generates efficient chaotic signals, and intuitively displays processes of the chaotic attractor, chaotic synchronization, period doubling and the road to chaos through the virtual oscilloscope, which is conducive to chaotic beginners' understanding of the basic characteristics and application of chaos. The electrical and mathematical analysis of the instrument is carried out by simulation, to explore the functions of each parameter, and helps beginners to understand its working principle more quickly and conduct experimental operations. It provides theoretical support for the improvement and optimization of Chua's circuit.

Novel bursting patterns and the bifurcation mechanism in a piecewise smooth Chua’s circuit with two scales

The aim of this paper is to investigate the influence of the coupling of two scales on the dynamics of a piecewise smooth dynamical system. A relatively simple model with two switching boundaries is taken as an example by introducing a nonlinear piecewise resistor and a harmonically changed electric source into a typical Chua’s circuit. Taking suitable values of the parameters, four different types of bursting oscillations are observed corresponding to different values of the exciting amplitude. Regarding the periodic excitation as a slow-varying parameter, equilibrium branches of the fast subsystem as well as the related bifurcations, such as fold bifurcation, Hopf bifurcation, period doubling bifurcation, nonsmooth Hopf bifurcation and nonsmooth fold limit cycle bifurcation, are explored with theoretical and numerical methods. With the help of the overlap of the transformed phase portrait and the equilibrium branches, the mechanism of the bursting oscillations can be analyzed in detail. It is found that for relatively small exciting amplitude, since the trajectory is governed by a smooth subsystem, only conventional bifurcations take place, leading to the transitions between the spiking states and quiescent states. However, with an increase of the exciting amplitude so that the trajectory passes across the switching boundaries, nonsmooth bifurcations occurring at the boundaries may involve the structures of attractors, leading to complicated bursting oscillations. Further increasing the exciting amplitude, the number of the spiking states decreases although more bifurcations take place, which can be explained by the delay effect of bifurcation