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Memristor and memcapacitor are two novel memristive devices. Memristive nonlinear elements behave like synapses in the nervous system. In this study, an original physical model of HP memristor is presented based on the movement of the boundary between the doped and undoped regions by causing the charged dopants to drift. Furthermore, a charge-controlled memcapacitor is used to design a novel hyperchaotic oscillator. It is found that the hyperchaotic oscillator, which is based on memristor and memcapacitor, can realize high-security data encryption. Then, the problem of controlling chaos is addressed in the proposed memcapacitor-based hyperchaotic memristor oscillator using a simple feedback control. Moreover, in this study, a novel approach is used to stabilize chaos using the L2–norm minimization method. The feedback control is applied to minimize the L2–norm of state variables as the cost function. An online particle swarm optimization (PSO) technique is developed to design the feedback control using L2–norm minimization. The sensitivity to initial condition is examined for different initial conditions. The proposed technique can be used for chaos stabilization in a complex dynamic system.

A new approach to adaptive control of chaos in a class of nonlinear discrete-time-varying systems, using a delayed state feedback scheme, is presented. It is discussed that such systems can show chaotic behavior as their parameters change. A strategy is employed for on-line calculation of the Lyapunov exponents that will be used within an adaptive scheme that decides on the control effort to suppress the chaotic behavior once detected. The scheme is further augmented with a nonlinear observer for estimation of the states that are required by the controller but are hard to measure. Simulation results for chaotic control problem of Jin map are provided to show the effectiveness of the proposed scheme.

This paper investigates chaos control for scalar delayed chaotic systems using sliding mode control strategy. Sliding surface design is based on delayed feedback controller. It is shown that the proposed controller can achieve stability for an arbitrary unstable fixed point (UPF) or unstable periodic orbit (UPO) with arbitrary period. The chaotic system used in this study to illustrate the theoretical concepts is the well known Mackey–Glass model. Simulation results show the effectiveness of the designed nonlinear sliding mode controller.

A gradient based approach for the design of set-point tracking adaptive controllers for nonlinear chaotic systems is presented. In this approach, Lyapunov exponents are used to select the controller gain. In the case of unknown or time varying chaotic plants, the Lyapunov exponents may vary during the plant operation. In this paper, an effective adaptive strategy is used for online identification of Lyapunov exponents and adaptive control of nonlinear chaotic plants. Also, a nonlinear observer for estimation of the states is proposed. Simulation results are provided to show the effectiveness of the proposed methodology.

In this paper, a method for estimating an attractor embedding dimension based on polynomial models and its application in investigating the dimension of Bremen climatic dynamics are presented. The attractor embedding dimension provides the primary knowledge for analyzing the invariant characteristics of the attractor and determines the number of necessary variables to model the dynamics. Therefore, the optimality of this dimension has an important role in computational efforts, analysis of the Lyapunov exponents, and efficiency of modeling and prediction. The smoothness property of the reconstructed map implies that, there is no self-intersection in the reconstructed attractor. The method of this paper relies on testing this property by locally fitting a general polynomial autoregressive model to the given data and evaluating the normalized one step ahead prediction error. The corresponding algorithms are developed in uni/multivariate form and some probable advantages of using information from other time series are discussed. The effectiveness of the proposed method is shown by simulation results of its application to some well-known chaotic benchmark systems. Finally, the proposed methodology is applied to two major dynamic components of the climate data of the Bremen city to estimate the related minimum attractor embedding dimension.