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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.

A new chaotic system is proposed to generate multiscroll chaotic attractors. The major method used is for the step function to act as a nonlinear function. To prove that the proposed system can generate multiscroll chaotic attractors, the equilibrium point, the time domain waveform and the phase diagram of the proposed system are calculated. Finally, the design of the hardware circuit produces experimental results at a maximum of 8-scroll hardware. Theoretical analysis, simulation and hardware experimental results are fully matched, which further proves the existence of the proposed system and the physical realization. This provides the possibility for future applications in engineering.

Based on the study on Jerk chaotic system, a multiscroll hyperchaotic system with hidden attractors is proposed in this paper, which has infinite number of equilibriums. The chaotic system can generate $N+M+2$ scroll hyperchaotic hidden attractors. The dynamic characteristics of the multiscroll hyperchaotic system with hidden attractors are analyzed by means of dynamic analysis methods such as Lyapunov exponents and bifurcation diagram. In addition, we have studied the synchronization of the system by applying an adaptive control method. The hardware experiment of the proposed multiscroll hyperchaotic system with hidden attractors is carried out using discrete components. The hardware experimental results are consistent with the numerical simulation results of MATLAB and the theoretical analysis results.

A chaotic system that can show multiscroll and megastable attractors is studied in this paper. Two cases of the system with periodic and quasi-periodic excitations are discussed. Various stabilities of the system determined by changing parameters and initial values are investigated for both cases. In Case-A of the proposed system, multiscroll attractors are shown for the various parameter values. In Case-B with quasi-periodic excitation, the system shows various multiscroll attractors. Dynamical properties of these two cases are studied using the bifurcation diagram and Lyapunov exponents.

A new conservative chaotic system with a cubic root is constructed in this paper. The system has no equilibria. An offset parameter is introduced into the system. By modulating different offset parameters and corresponding initial conditions, multiple coexisting conservative chaotic attractors can be generated consequently. By replacing the offset parameter with an appropriate sign function, multiscroll conservative chaotic attractors can be generated effectively by connecting multiple coexisting chaotic attractors based on offset boosting. Moreover, the number of scrolls tend to be infinite. Finally, a novel chaotic circuit with a cubic root is designed successfully by connecting two multipliers in opposite directions. The hardware implementation of the chaotic circuit is also completed to further verify the existence of conservative chaos and the consistency with the numerical simulations.

The study of chaotic systems with special properties addresses one of the ongoing research topics. In this paper, we introduce a new class of third-order chaotic systems possessing a cyclic symmetry obeying unidirectional or mutual coupling. These new models are built by considering nonlinearities with three, four, or five segments and are distinguished from each other by the topological structure of the associated chaotic attractor. The projection of the novel chaotic attractors on certain planes reveals their multiscroll or multiwing character. For illustration, one of these models is studied in detail using analytical and numerical methods. The mechanism giving rise to the establishment of the chaotic regime starting from the state of equilibrium under the variation of a parameter is described using bifurcation diagrams, phase portraits, basins of attraction as well as the maximum Lyapunov exponent. Several zones of parameters are identified where the model experiences two or more attractors (i.e. multistability). In order to demonstrate the practical feasibility of the proposed circulant models, a series of experimental measurements are carried out using a physical implementation with an Arduino microcontroller.