Stabilization of the Fractional-Order Chua Chaotic Circuit via the Caputo Derivative of a Single Input

A modified fractional-order Chua chaotic circuit is proposed in this paper, and the chaotic attractor is obtained for q=0.98. Based on the Mittag-Leffler function in two parameters and Gronwall’s Lemma, two control schemes are proposed to stabilize the modified fractional-order Chua chaotic system via the Caputo derivative of a single input. The numerical simulation shows the validity and feasibility of the control scheme

New Methods of Finite-Time Synchronization for a Class of Fractional-Order Delayed Neural Networks

Finite-time synchronization for a class of fractional-order delayed neural networks with fractional order α, 0<α≤1/2 and 1/2<α<1, is investigated in this paper. Through the use of Hölder inequality, generalized Bernoulli inequality, and inequality skills, two sufficient conditions are considered to ensure synchronization of fractional-order delayed neural networks in a finite-time interval. Numerical example is given to verify the feasibility of the theoretical results

Dynamical Systems

Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and electrical and mechanical structures. Complex systems are often composed of a large number of interconnected and interacting entities, exhibiting much richer global scale dynamics than the properties and behavior of individual entities. Complex systems are studied in many areas of natural sciences, social sciences, engineering and mathematical sciences. This special issue therefore intends to contribute towards the dissemination of the multifaceted concepts in accepted use by the scientific community. We hope readers enjoy this pertinent selection of papers which represents relevant examples of the state of the art in present day research. [...

Synchronization of a Class of Fractional-Order Chaotic Neural Networks

The synchronization problem is studied in this paper for a class of fractional-order chaotic neural networks. By using the Mittag-Leffler function, M-matrix and linear feedback control, a sufficient condition is developed ensuring the synchronization of such neural models with the Caputo fractional derivatives. The synchronization condition is easy to verify, implement and only relies on system structure. Furthermore, the theoretical results are applied to a typical fractional-order chaotic Hopfield neural network, and numerical simulation demonstrates the effectiveness and feasibility of the proposed method