Decentralized adaptive coupling synchronization of fractional-order complex-variable dynamical networks

Outer Synchronization of Drive‐Response Complex‐Valued Complex Networks via Intermittent Pinning Control

“…Our first basic assumption will be used throughout this paper to deal with the nonlinearity of the systems. Assumption 1 (See [19]). For some given matrix Γ, it is assumed there exists a positive-definite diagonal matrix P � diag p 1 , p 2 , .…”

“…e relative conclusion in this letter involves realdomain and complex-domain networks. Sun and Xu et al investigated the synchronization of complex-variable networks with fractional order [18,19]. Among them, Sun et al mainly discussed the real combination asymptotical synchronization of three fractional-order complex-variable chaotic systems based on the related theories [18], and Xu et al used the fractional-order techniques and the correlation control strategy to implement fractional-order complex-domain network synchronization [19].…”

Complex Modified Projective Synchronization of Fractional-Order Complex-Variable Chaotic System with Unknown Complex Parameters

“…Lemma 2. [42] Let z ∈ C n be a differentiable complex-valued vector. Then, ∀t ≥ t 0 and α ∈ (0, 1], the following inequality holds…”

“…[ 42 ] Let be a differentiable complex-valued vector. Then, and , the following inequality holds where is a constant positive definite Hermitian matrix.…”

Stabilization of a class of fractional-order nonautonomous systems using quadratic Lyapunov functions

“…Fractional calculus, as a mathematical tool dealing with derivatives and integrals of arbitrary orders, has played a central role in physics [1], differential and integral equations [2], signal processing [3], human relationships [4], image encryption [5], thermal conductivity [6], electrical circuits [7], dynamical models [8], nonlinear control systems [9], complex networks [10], and so on. One of very important areas of application is nonlinear control systems.…”