Abstract
A projective synchronization scheme for a kind of n-dimensional discrete dynamical system is proposed by means of a linear feedback control technique. The scheme consists of master and slave discrete dynamical systems coupled by linear state error variables. A kind of novel 3-D chaotic discrete system is constructed, to which the test for chaos is applied. By using the stability principles of an upper or lower triangular matrix, two controllers for achieving projective synchronization are designed and illustrated with the novel systems. Lastly some numerical simulations are employed to validate the effectiveness of the proposed projective synchronization scheme.
Highlights
Nearby trajectories of a chaotic system may experience exponential divergence, but two or more coupled dissipative chaotic systems evolving in synchrony might appear quite surprising
A variety of control methods for projective chaos synchronization have been proposed for various kinds of nonlinear chaotic systems
By using linear state error feedback control technology, Xin et al [2,3,23] studied the projective synchronization for three kinds of chaotic fractional-order systems
Summary
Nearby trajectories of a chaotic system may experience exponential divergence, but two or more coupled dissipative chaotic systems evolving in synchrony might appear quite surprising. A variety of control methods for projective chaos synchronization have been proposed for various kinds of nonlinear chaotic systems. The advantage of the linear feedback controller is that it is robust and linear, and it is easier to design and implement for chaos synchronization than the abovementioned schemes. By using linear state error feedback control technology, Xin et al [2,3,23] studied the projective synchronization for three kinds of chaotic fractional-order systems. It is not difficult for us to extend the mentioned projective synchronization scheme from fractional-order systems to discrete dynamical systems.
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