Progress in Automation, Robotics and Measuring Techniques
Book Preface
Dynamical systems described by fractional order differential or difference equations have been investigated in several areas such as viscoelasticity, electrochemistry, diffusion processes, control theory, electrical engineering, etc. The problems of analysis and synthesis of dynamic systems described by fractional order differential (or difference) equations recently have considerable attention, see monographs [8, 13, 15, 17‒19], for example.
Many non-linear dynamical systems have behavior known as chaos. Chaos is a very interesting non-linear phenomenon. Chaotic systems are deterministic and highly sensitive on initial condition and system parameters. There are many chaotic systems, e.g. in paper [16] was introduced Pandey-Baghel-Singh chaotic system of integer order. Synchronization of chaos is a very interesting problem, enjoying a wide interest, for example, in control technology, cryptography, communications [9, 20], etc.
The problem of synchronization of chaos recently has been intensively studied in many papers, see for example [3, 4, 7, 10, 11, 25] for systems of integer order and [2, 6, 12, 14, 17, 21, 22] for system of fractional order. In the paper [2] the method of the synchronization of two coupled general chaotic fractional order Van der Pol- Duffing systems with a unidirectional linear error feedback coupling is presented.
In this paper we consider the modified Pandey-Baghel-Singh oscillator of fractional order. Chaotic behavior of this system will be analyzed for different values of fractional orders. Simple sufficient condition for synchronization of two such systems with non-commensurate fractional orders via master/slave configuration with linear coupling will be given. The proposed condition is obtained in a similar way as in the paper [2] using the Lyapunov and Gershgorin stability theory.
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