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Chaos generalized synchronization of an inertial tachometer with new Mathieu-Van der Pol systems as functional system by GYC partial region stability theory. (English) Zbl 1250.34044

The authors implement a form of generalised synchronisation of a pair of identical chaotic ODE systems. Generalised synchronisation means that there is a functional relationship between the variables of one system and the variables of the other system. The synchronisation is implemented by driving one system by a signal which depends on the state of the driving system, the state of the driven system, and the value of an “error” function which is determined by the form of the functional relationship that one is trying to obtain. The exposition of the theory is difficult to follow. The results are demonstrated on a pair of “inertial tachometer” systems, and a pair of four ODEs formed by coupling a Mathieu equation with a van der Pol equation.

MSC:

34D06 Synchronization of solutions to ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
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