Narrow Results

In this paper, a fractional-order hyperchaotic system evolved from Liu system is proposed. Based on the theory of fractional calculus, a novel circuit diagram is designed for hardware implementation of the fractional-order hyperchaotic Liu system. Furthermore, implementation results reveal that hyperchaos can be generated in the hyperchaotic Liu system with the system order as low as 3.6 and numerical analysis results demonstrate that the lowest order of the fractional-order Liu system is 0.4.

In this paper, a novel four-wing chaotic system is constructed based on the Sprott-A system. The novel system contains three nonlinearly quadratic terms, which have rich dynamics such as four-wing hidden attractors, hidden extreme multistability and transient transitions. It is found that this system has high complexity by spectral entropy analysis. In addition, a corresponding hardware analog circuit is designed based on this system by operational amplifiers and multipliers. The experimental results agree with those of the theoretical analysis and confirm that this system is practically feasible. This system will have a good application value in secure communication and cryptography.

This paper presents a new four-dimensional chaotic system with three nonlinearities and two equilibria. The most striking feature of the new system is that it has different types of asymmetric coexisting attractors. Simulation experiments are used to study the complex dynamic behaviors of the system. The chaos, period-doubling bifurcation, coexisting attractors with respect to system parameters and initial values are found in the system. It shows that the system has coexisting chaotic attractors, coexisting periodic attractors, coexisting chaotic and periodic attractors. The electronic circuit is applied to implement the chaotic attractor and coexisting attractors for studying the physical significance of the system. In addition, we consider the synchronization of the system by using the impulsive control method. Some synchronization criteria are established via theoretical analysis and simulation example.

The purpose of this work is to introduce a novel 4D chaotic system and investigate its multistability. The novel system has an unstable origin and two stable symmetrical hyperbolic equilibria. When the parameter increases across a critical value, the equilibria lose their stability and double Hopf bifurcations occur with the appearance of limit cycles. A pair of point, periodic, chaotic attractors are observed in the system from different initial values for given parameters. The chaos of the system is yielded via period-doubling bifurcation. A double-scroll chaotic attractor is numerically observed as well. By using the electronic circuit, the chaotic attractor of the system is realized. The control problem of the system is reported. An effective controller is designed to stabilize the system.

This paper constructs a novel memristive hyperchaotic system by introducing the flux-controlled memristor to an extended jerk system. The memristive system has two equilibria and coexists two symmetric hyperchaotic attractors. The dynamic behaviors of the system are studied through bifurcation analysis. The analog circuit design and microcontroller-based experimental implementation of the system are presented. The synchronization of the system is realized by using the adaptive control technique. The sufficient conditions for synchronization are established via theoretical and numerical analysis.

This paper introduces a new five-dimensional hyper-chaotic system with hyper-chaotic attractors. Its typical dynamical behaviors are also analyzed. The existence of hyper-chaotic attractors has been verified through Multisim and MATLAB simulations as well as circuit experiments. The Lyapunov stability theory is used to realize the stagger and adaptive synchronization of the system. During this process, the two methods are used to demonstrate the feasibility and compare the synchronization speed in different cases. The experimental results show that the staggered synchronization will converge to the synchronized state in a short time than another. This hyper-chaotic system is implemented with simple physical components to illustrate its correctness and rationality.

This work shows the experimental implementation of a chaotic communication system based on two Chua's oscillators which are synchronized by Hamiltonian forms and observer approach. The chaotic communication scheme is realized by using the commercially available positive-type second generation current conveyor (CCII+), which is included into the AD844 device. As a result, experimental measurements are provided to demonstrate the suitability of the CCII+ to implement chaotic communication systems.

In this paper, a 4D hyperchaotic Chua system both with piecewise-linear nonlinearity and with smooth and piecewise smooth cubic nonlinearity is introduced, based on state feedback control. Dynamical behaviors of this hyperchaotic system are further investigated, including Lyapunov exponents spectrum, bifurcation diagram and solution of state equations. Theoretical analysis and numerical results show that this system can generate multiscroll hyperchaotic attractors. In addition, a circuit is designed for 4D hyperchaotic Chua system such that the double-scroll and 3-scroll hyperchaotic attractors can be physically obtained, demonstrating the effectiveness of the proposed simulation-based techniques.

An unique 4D autonomous chaotic system with signum function term is proposed in this paper. The system has four unstable equilibria and various types of coexisting attractors appear. Four-wing and four-scroll strange attractors are observed in the system and they will be broken into two coexisting butterfly attractors and two coexisting double-scroll attractors with the variation of the parameters. Numerical simulation shows that the system has various types of multiple coexisting attractors including two butterfly attractors with four limit cycles, two double-scroll attractors with a limit cycle, four single-scroll strange attractors, four limit cycles with regard to different parameters and initial values. The coexistence of the attractors is determined by the bifurcation diagrams. The chaotic and hyperchaotic properties of the attractors are verified by the Lyapunov exponents. Moreover, we present an electronic circuit to experimentally realize the dynamic behavior of the system.

In this paper, a new four-dimensional chaotic flow is proposed. The system has a cyclic symmetry in its structure and shows a complicated, chaotic attractor. The dynamical properties of the system are investigated. The system shows multistability in an interval of its parameter. Fractional order model of the proposed system is discussed in various fractional orders. Bifurcation analysis of the fractional order system shows that it has a kind of multistability like the integer order system, which is a very rare phenomenon. Circuit realization of the proposed system is also carried out to show that it is usable for engineering applications.

Compared with dissipative chaos, conservative chaos is more suitable for information encryption since it does not have attractors, therefore, it is important to construct different complicated conservative chaotic systems. This paper reports an effective approach to construct a class of 4D conservative systems based on the formalism of a generalized Hamiltonian system. Based on the construction approach, several example systems including one hyperspatial multicluster chaotic system are proposed, and different cluster-shaped chaotic flows are discovered in these example systems. The only difference of these example systems is their Hamiltonians, whose local minimum points directly determine the number and position of these cluster-shaped conservative chaotic flows. Numerical simulations vividly demonstrate that different cluster-shaped chaotic flows really move around different local centers, i.e. the local minimum points of the Hamiltonian. In addition, an analog circuit is designed and simulated in NI Multisim to confirm the existence of multicluster conservative chaotic flows at the physical level.