Current Trends on Fractional-Order Systems: Bifurcations, Synchronization, and Chaos

Dear Colleagues,

Fractional calculus is an exciting and powerful tool for addressing problems involving non-integer order integration and differentiation. Since the pioneering work of the Norwegian mathematician Niels Henrik Abel (1802-1829)—who introduced a rather general framework for fractional calculus while solving the tautochrone problem—many researchers have been attracted by this branch of mathematics and its applications in science and technology. In fact, from a Dynamical Systems perspective, fractional calculus has helped us to understand and to model nonlinear phenomena, for example, chaotic behavior, synchronization, bifurcations, and population dynamics, among others. Hence, nowadays, the following words of H. T. Davis, a former professor at the University of New Mexico, are more valid than ever: “The great elegance that can be secured by the proper use of fractional operators and the power which they have in the solution of complicated functional equations should more than justify a more general recognition and use”.

This Special Issue aims to provide a forum for presenting state-of-the-art theoretical, numerical, and experimental results regarding the modeling, analysis, and implementation of dynamical systems described by fractional order differential equations as well as the study of nonlinear phenomena, for example, chaos, bifurcations, and synchronization, occurring in (networks of) fractional order systems, emerging either as a consequence of the interaction among them or due to a variation in the fractional order of the derivative.

The topics covered in this Special Issue include but are not limited to the following:

• Modeling of nonlinear phenomena via fractional order differential equations;
• Fractional-order chaotic systems;
• Synchronization of (networks of) fractional-order dynamical systems;
• Emergent behavior;
• Bifurcations;
• Integer and fractional-order dynamic couplings;
• Periodic solutions and fractional order oscillators;
• Stability and multi-stability;
• Complex networks;
• Fractional order neural networks;
• Applications of fractional order ordinary differential equations;
• Influence of the fractional-order of a system on the onset of bifurcations and chaos.

Dr. Joaquin Alvarez
Dr. J. Pena-Ramirez
Guest Editors

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• stability
• oscillators
• complex networks
• chaos
• bifurcation
• synchronization
• emergent behavior
• fractional order neural networks