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Exponential synchronization of memristive Cohen–Grossberg neural networks with mixed delays

TLDR
By investigating the global exponential synchronization of the alternative system, the corresponding synchronization criteria of the considered memristor-based Cohen–Grossberg neural networks are obtained.
Abstract
This paper concerns the problem of global exponential synchronization for a class of memristor-based Cohen–Grossberg neural networks with time-varying discrete delays and unbounded distributed delays. The drive-response set is discussed. A novel controller is designed such that the response (slave) system can be controlled to synchronize with the drive (master) system. Through a nonlinear transformation, we get an alternative system from the considered memristor-based Cohen–Grossberg neural networks. By investigating the global exponential synchronization of the alternative system, we obtain the corresponding synchronization criteria of the considered memristor-based Cohen–Grossberg neural networks. Moreover, the conditions established in this paper are easy to be verified and improve the conditions derived in most of existing papers concerning stability and synchronization for memristor-based neural networks. Numerical simulations are given to show the effectiveness of the theoretical results.

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References
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Optimization and nonsmooth analysis

TL;DR: The Calculus of Variations as discussed by the authors is a generalization of the calculus of variations, which is used in many aspects of analysis, such as generalized gradient descent and optimal control.
Journal ArticleDOI

The missing memristor found

TL;DR: It is shown, using a simple analytical example, that memristance arises naturally in nanoscale systems in which solid-state electronic and ionic transport are coupled under an external bias voltage.
Journal ArticleDOI

Memristor-The missing circuit element

TL;DR: In this article, the memristor is introduced as the fourth basic circuit element and an electromagnetic field interpretation of this relationship in terms of a quasi-static expansion of Maxwell's equations is presented.
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Differential Equations with Discontinuous Righthand Sides

TL;DR: The kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics, algebraic geometry interacts with physics, and such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.
Journal ArticleDOI

Absolute stability of global pattern formation and parallel memory storage by competitive neural networks

TL;DR: It remains an open question whether the Lyapunov function approach, which requires a study of equilibrium points, or an alternative global approach, such as the LyAPunov functional approach, will ultimately handle all of the physically important cases.
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