Projective synchronization of chaotic fractional-order energy resources demand–supply systems via linear control

Existence and Globally Asymptotic Stability of Equilibrium Solution for Fractional-Order Hybrid BAM Neural Networks with Distributed Delays and Impulses

“…At the same time, fractional-order differential equations have been proved to be an excellent tool in the modelling of many phenomena [9][10][11]. Recently, some important advances on dynamical behaviors such as chaos phenomena, Hopf bifurcation, synchronization control, and stabilization problems for fractional-order systems or fractional-order practical models have been reported in [12][13][14][15][16]. These proposed results show the superiority and importance of fractional calculus and effectively motivate the development of new applied fields.…”

Adaptive Switched Generalized Function Projective Synchronization between Two Hyperchaotic Systems with Unknown Parameters

“…Recently, Du et al [30] discussed a new type of synchronization phenomenon, modified function projective synchronization (MFPS), in which the drive and response systems could be synchronized up to a desired scaling function matrix. Many of these synchronization schemes have been applied to investigate chaotic or fractional chaotic systems [37][38][39][40][41][42][43][44]. More recently, Yu and Li [31] have proposed a new synchronization scheme by choosing a more generalized scaling function matrix, called generalized function projective synchronization (GFPS), which is an extension of all the aforementioned projective synchronization schemes.…”

Projective Synchronization of Chaotic Discrete Dynamical Systems via Linear State Error Feedback Control

“…Chen et al [21,22] also did some sound work designing controllers which are less than the number of dimensions of the 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. It is not difficult for us to extend the mentioned projective synchronization scheme from fractional-order systems to discrete dynamical systems.…”

“…Furthermore the synchronization error system between the coupled chaotic systems may be asymptotically stable if some suitable control techniques are implemented on them. As a common multi-disciplinary phenomenon, chaos synchronization has broad range applications, such as secure communication [1], OPEN ACCESS chaotic economic systems [2], WINDMI systems [3], hyperchaotic complex-variable systems [4], chaotic complex networks [5], fractional-order chaotic neural networks [6], etc.…”