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In this paper, we have proposed a novel three-dimensional Lorenz-like chaotic system. Some basic properties of the system, such as dynamical behaviors, bifurcation diagram. Lyapunov exponents and Poincare mapping are investigated either analytically or numerically. Furthermore, the control problem of the new chaotic system was studied via nonlinear backstepping method. The single backstepping control input was designed according to Lyapunov stability criterion. Numerical simulations are carried out in order to demonstrate the effectiveness of the proposed control design. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with designing a sliding mode controller (SMC) for a fractional-order chaotic financial system. Using the sliding mode control technique, a sliding surface is determined. The sliding mode control law is derived to make the states of the fractional-order financial system asymptotically stable. The designed control scheme is robust against the system’s uncertainty and guarantees the property of asymptotical stability in the presence of an external disturbance. An illustrative simulation result is given to demonstrate the effectiveness of the proposed sliding mode control design. [Copyright &y& Elsevier]

A new four-dimensional quadratic smooth autonomous chaotic system is presented in this paper, which can exhibit periodic orbit and chaos under the conditions on the system parameters. Importantly, the system can generate one-, two-, three- and four-scroll chaotic attractors with appropriate choices of parameters. Interestingly, all the attractors are generated only by changing a single parameter. The dynamic analysis approach in the paper involves time series, phase portraits, Poincar'e maps, a bifurcation diagram, and Lyapunov exponents, to investigate some basic dynamical behaviours of the proposed four-dimensional system. [ABSTRACT FROM AUTHOR]

Abstract: This Letter presents a novel four-dimensional complex nonlinear autonomous system. This system has very rich dynamics and can exhibit hyperchaos, chaos, quasi-periodic and periodic behavior. Applying two symmetrical initial conditions, this system can generate two coexist double-scroll hyperchaotic attractors. More interestingly, this new system can generate not only a four-scroll hyperchaotic but also a four-scroll chaotic attractor. This nonlinear complex system is analyzed by Lyapunov exponent spectrum, bifurcation diagram and Poincaré mapping. [Copyright &y& Elsevier]

Abstract: In this Letter a novel three-dimensional autonomous chaotic system is proposed. Of particular interest is that this novel system can generate two, three and four-scroll chaotic attractors with variation of a single parameter. By applying either analytical or numerical methods, basic properties of the system, such as dynamical behaviors (time history and phase diagrams), Poincaré mapping, bifurcation diagram and Lyapunov exponents are investigated to observe chaotic motions. The obtained results clearly show that this is a new chaotic system which deserves further detailed investigation. [Copyright &y& Elsevier]