Abstract
In this article, without dividing a complex-valued neural network into two real-valued subsystems, the global synchronization of fractional-order complex-valued neural networks (FOCVNNs) is investigated by the Lyapunov direct method rather than the real decomposition method. It is worth mentioning that the partial adaptive control and partial linear feedback control schemes are introduced, by constructing suitable Lyapunov functions, some improved synchronization criteria are derived with the help of fractional differential inequalities and L’Hospital rule as well as some complex analysis techniques. Finally, simulation results are given to demonstrate the validity and feasibility of our theoretical analysis.
Highlights
During the past few years, real-valued neural networks (RVNNs) have attracted much attention due to the background of a wide range of applications such as associative memory, pattern recognition, image processing and model identification [1,2,3,4,5,6]
In [32], Li et al designed a linear feedback controller and adaptive controller, and the complete synchronization and quasi-projective synchronization criteria for fractional-order complex-valued neural networks (FOCVNNs) were derived by using the Lyapunov direct method, respectively
Motivated by the above discussions, this paper investigates the global synchronization for the addressed FOCVNNs by partial control
Summary
During the past few years, real-valued neural networks (RVNNs) have attracted much attention due to the background of a wide range of applications such as associative memory, pattern recognition, image processing and model identification [1,2,3,4,5,6]. Many researchers consider fractional-order complex-valued neural networks (FOCVNNs), and some remarkable results on bifurcation [27] and stability [28] as well as synchronization [29,30,31] have been reported. In [32], Li et al designed a linear feedback controller and adaptive controller, and the complete synchronization and quasi-projective synchronization criteria for FOCVNNs were derived by using the Lyapunov direct method, respectively. The main contributions of this paper are the following three aspects: (1) The partial adaptive control and partial linear feedback control schemes are first proposed to realize synchronization of FOCVNNs. 3, the partial adaptive control and partial linear feedback control schemes are proposed to achieve synchronization for the addressed FOCVNNs. In Sect. Lemma 2 ([37]) Let z(t) ∈ Cn be a differentiable complex-valued vector, the following inequality holds: Dqt zH (t)Pz(t).
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