A novel 4-D hyperchaotic four-wing system with a saddle–focus equilibrium is introduced in this brief. The qualitative analysis of the proposed system confirms its complex dynamic behavior, which is studied by using well-known numerical tools of nonlinear theory, such as the bifurcation diagram, Lyapunov exponents, Poincare maps, and phase portraits. Furthermore, the novel hyperchaotic system is experimentally emulated by an electronic circuit, and its dynamic behavior is studied to confirm the feasibility of the theoretical model.

A Novel Four-Dimensional Hyperchaotic Four-Wing System With a Saddle–Focus Equilibrium

Based on fractional transfer function approximation in frequency domain, the paper firstly discusses the fractional form of a four-wing autonomous integral-order chaotic system, and finds some chaotic attractors in the different orders of the fractional-order system. The chaotic attractors can be found when the order of the fractional-order system is varied from 1.5 to 2.7, especially in the fractional-order system of the order as low as 2.7, and various chaotic behaviors occur when varying four different system parameters. Some bifurcation diagrams and phase portraits including the four-wing chaotic attractors, the two-wing chaotic attractors, and some periodic orbits are given to verify the chaotic behaviors of the fractional-order system. Then, based on the method of topological horseshoe analysis adopted in many integer-order chaotic systems, a topological horseshoe is found to prove the existence of chaos in the fractional-order system of the order as low as 2.7. At last, an analog circuit is designed to confirm the chaotic dynamics of fractional-order system.

Chaotic Characteristics Analysis and Circuit Implementation for a Fractional-Order System

The paper first discusses a newly reported fractional-order Lu system of order as low as 2.7 and shows its chaotic characteristics by numerical simulations. Then by using the topological horseshoe theory and computer-assisted proof, the existence of chaos in the system is verified theoretically. Finally, an analog hardware circuit is made for the fractional-order system, and the observed results demonstrate that the fractional-order Lu system is chaotic in physical experiment.

Topological horseshoe analysis and circuit realization for a fractional-order Lü system

In this work, active control method is proposed for controlling and synchronising seven-dimensional (7D) hyperchaotic systems. The seven-dimensional hyperchaotic system is considered for the implementation. Seven-dimensional hyperchaotic system is also investigated via time series, phase portraits and bifurcation diagrams. For understanding the impact of active controllers on global asymptotic stability of synchronisation and control errors, the Lyapunov function is used. Numerical analysis is done to reveal the effectiveness of applied active control method and the results are discussed.

Control and synchronisation of a novel seven-dimensional hyperchaotic system with active control

The paper first analyzes a newly reported three-dimensional four-wing chaotic attractor, and observes all kinds of attractors, including periodic and chaotic, by numerical simulation. Then, the chaotic characteristic of the system is proved by investigating the existence of a topological horseshoe in it, based on the topological horseshoe theory. At last, an electronic circuit is designed to implement the chaotic system. The results of circuit experiment coincided well with those of numerical simulation.

Topological horseshoe analysis and the circuit implementation for a four-wing chaotic attractor

By introducing an additional state feedback into a three-dimensional autonomous chaotic attractor Lu system, this paper presents a novel four-dimensional continuous autonomous hyper-chaotic system which has only one equilibrium. There are only 8 terms in all four equations of the new hyper-chaotic system, which may be less than any other four-dimensional continuous autonomous hyper-chaotic systems generated by three-dimensional (3D) continuous autonomous chaotic systems. The hyper-chaotic system undergoes Hopf bifurcation when parameter c varies, and becomes the 3D modified Lu system when parameter k varies. Although the hyper-chaotic system does not undergo Hopf bifurcation when parameter k varies, many dynamic behaviours such as periodic attractor, quasi periodic attractor, chaotic attractor and hyper-chaotic attractor can be observed. A circuit is also designed when parameter k varies and the results of the circuit experiment are in good agreement with those of simulation.

A novel one equilibrium hyper-chaotic system generated upon Lü attractor

This paper presents a non-autonomous hyper-chaotic system, which is formed by adding a periodic driving signal to a four-dimensional chaotic model extended from the Lorenz system. The resulting non-autonomous hyper-chaotic system can display any dynamic behaviour among the periodic orbits, intermittency, chaos and hyper-chaos by controlling the frequency of the periodic signal. The phenomenon has been well demonstrated by numerical simulations, bifurcation analysis and electronic circuit realization. Moreover, the system is concrete evidence for the presence of Pomeau–Manneville Type-I intermittency and crisis-induced intermittency. The emergence of a different type of intermittency is similarly subjected to the frequency of periodic forcing. By statistical analysis, power scaling laws consisting in different intermittency are obtained for the lifetime in the laminar state between burst states.

陈增强

Papers

A novel one equilibrium hyper-chaotic system generated upon Lü attractor

Circuit implementation and multiform intermittency in a hyper-chaotic model extended from the Lorenz system