Abstract
This research discuss the existence, uniqueness, asymptotic stability, and global asymptotic synchronization of a class of Caputo variable-order neural networks with time-varying external inputs. Theory of contraction mapping is used to establish a sufficient condition for determining the existence and uniqueness of the equilibrium point. Using the variable fractional Lyapunov approach, we investigate the asymptotic stability of the unique equilibrium. Synchronization of variable-order chaotic networks is also studied using an effective controller. Three numerical examples are provided to show the efficacy of the results obtained.
Highlights
Fractional calculus is an old mathematical concept that was created long ago by mathematicians such as Leibniz, Liouville, Riemann, and others
We focus on the existence, uniqueness, asymptotic stability and global asymptotic synchronization analysis of fractional variable-order neural networks with time-varying external inputs, where the variable-order fractional derivatives is in Caputo meaning
This study is devoted to investigating the existence, uniqueness, asymptotic stability and synchronization of variable-order fractioanl neural networks with time-varying external inputs with the use of the Caputo variableorder fractional derivative
Summary
Fractional calculus is an old mathematical concept that was created long ago by mathematicians such as Leibniz, Liouville, Riemann, and others. Even though the constant fractional calculus concept may handle certain extremely significant physical issues, it cannot capture major classes of physical events in which the order is a function of either dependent or independent variables. As a result, it implies that there are categories of physical problems that are better characterized by variable-order operators [9][4]. We focus on the existence, uniqueness, asymptotic stability and global asymptotic synchronization analysis of fractional variable-order neural networks with time-varying external inputs, where the variable-order fractional derivatives is in Caputo meaning.
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