Yuxia Li

GENERATING HYPERCHAOS VIA STATE FEEDBACK CONTROL

In this letter, a simple nonlinear state feedback controller is designed for generating hyperchaos from a three-dimensional autonomous chaotic system. The hyperchaotic system is not only demonstrated by computer simulations but also verified with bifurcation analysis, and is implemented experimentally via an electronic circuit.

Chaos and hyperchaos in fractional-order cellular neural networks

In this paper, a fractional-order four-cell cellular neural network is proposed and the complex dynamical behaviors of such a network are investigated by means of numerical simulations. Several varieties of interesting dynamical behaviors, such as periodic, chaotic and hyperchaotic motions, are displayed. In addition, it can be found that the network does exhibit hyperchaotic phenomena over a wide range of values of some specified parameter. The existence of chaotic and hyperchaotic attractors is verified with the related Lyapunov exponent spectrum, bifurcation diagram and phase portraits. Meanwhile, the Lyapunov exponents and Poincare sections are calculated for some typical parameters, respectively.

Hyperchaos evolved from the generalized Lorenz equation

SUMMARY In this letter, a new hyperchaotic system is formulated by introducing an additional state into the third-order generalized Lorenz equation. The existence of the hyperchaos is veried with bifurcation analysis, and the bifurcation routes from periodic, quasi-periodic, chaotic and hyperchaotic evolutions are observed. Various attractors are illustrated not only by computer simulation but also by the realization of an electronic circuit. Copyright ? 2005 John Wiley & Sons, Ltd.

Controlling a unified chaotic system to hyperchaotic

This brief presents a simple technique using a sinusoidal parameter perturbation control input to drive a unified chaotic system to hyperchaotic. The original chaotic system is a three-dimensional autonomous system that has a broad spectrum of chaotic behaviors with the Lorenz and the Chen systems as two extremes of the spectrum. The control input is a simple sinusoidal function cos(/spl omega/t) with a constant parameter /spl omega/. The hyperchaotic system is not only demonstrated by computer simulations but also verified with bifurcation analysis and implemented via an electronic circuit.

A new hyperchaotic Lorenz-type system: Generation, analysis, and implementation

A new four-dimensional continuous-time autonomous hyperchaotic Lorenz-type system is introduced and analyzed. This hyperchaotic system is not only visualized by computer simulation but also verified with bifurcation analysis and realized with an electronic circuit. Moreover, explicit formulae for estimating the ultimate bound and positive invariant set of the system are derived by constructing a family of generalized Lyapunov functions. The findings and results of this paper have good potential in control and synchronization of hyperchaos and their engineering applications. Copyright

Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays

In this paper, a class of complex-valued neural network model with discrete and distributed delays is proposed. Regarding the discrete time delay as the bifurcating parameter, the problem of Hopf bifurcation in the newly-proposed complex-valued neural network model is investigated under the assumption that the activation function can be separated into its real and imaginary parts. Based on the normal form theory and center manifold theorem, some sufficient conditions which determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are established. Finally, a numerical example is given to illustrate the validity of the theoretical results.

Consensus of third-order nonlinear multi-agent systems

This paper considers the consensus problem of third-order nonlinear multi-agent systems with a fixed communication topology. A consensus protocol is proposed for solving such a problem. By a transformation, the consensus problem is converted to a stability problem, then sufficient consensus criteria are obtained by proposing a novel Lyapunov function. It is shown that consensus can be achieved for a sufficiently large feedback gain, provided that certain quadratic inequalities with respect to two parameters are satisfied. Finally, the effectiveness of the theoretical results is demonstrated through an example.

Global exponential stability for switched memristive neural networks with time-varying delays

This paper considers the problem of exponential stability for switched memristive neural networks (MNNs) with time-varying delays. Different from most of the existing papers, we model a memristor as a continuous system, and view switched MNNs as switched neural networks with uncertain time-varying parameters. Based on average dwell time technique, mode-dependent average dwell time technique and multiple Lyapunov-Krasovskii functional approach, two conditions are derived to design the switching signal and guarantee the exponential stability of the considered neural networks, which are delay-dependent and formulated by linear matrix inequalities (LMIs). Finally, the effectiveness of the theoretical results is demonstrated by two numerical examples.

Design of fuzzy state feedback controller for robust stabilization of uncertain fractional-order chaotic systems

Abstract In this paper, the stabilization problem of uncertain fractional-order chaotic systems is investigated in the case where the fractional order α satisfies 0 α 1 and 1 ≤ α 2 . Firstly, the uncertain fractional-order chaotic system is described by the so-called fractional-order T–S fuzzy model, and then the fuzzy state feedback controller is correspondingly designed. Secondly, sufficient conditions are derived for the robust asymptotical stability of the closed-loop control systems in those two cases. These criteria are expressed in terms of linear matrix inequalities (LMIs), and the feedback gain matrices can be formulated into the solvability of the relevant LMIs. The proposed controller overcomes some defects in traditional control techniques and is easy to implement. Finally, two numerical examples are presented to demonstrate the effectiveness and the feasibility of the robust stabilizing controller and the robust asymptotical stability criteria.

Complex nonlinear dynamics in fractional and integer order memristor-based systems

Abstract In this paper, a fractional-order (and an integer-order) memristor-based system with the flux-controlled memristor characterized by smooth quadratic nonlinearity is proposed and detailed dynamical analysis is carried out by means of theoretical and numerical methods. To be more specific, stability of each equilibrium point in the equilibrium set is analyzed for the integer-order memristive system. Meanwhile, dynamical behavior depending on the initial states of the memristor is investigated and dynamical bifurcation depending on the slope of the memductance function is also considered. The bifurcation analysis is verified by numerical methods, including phase portraits, bifurcation diagrams, Lyapunov exponents spectrum, and Poincare mappings. For the fractional-order case, based on the fractional-order stability theory, stability analysis is carried out just for a certain equilibrium point. Moreover, bifurcation behavior depending on the incommensurate order is discussed by virtue of numerical methods based on the Adams–Bashforth–Moulton algorithm. This paper indicates how the fractional order model and the initial state of the memristor extend the dynamical behaviors of the traditional chaotic systems.