State-dependent impulsive Cohen-Grossberg neural networks with time-varying delays

2016-01-01
Sayli, Mustafa
YILMAZ, ENES
In this paper, a more general class of state-dependent impulsive Cohen-Grossberg neural networks having variable coefficients with time-varying delays is addressed. By means of B-equivalence method, we reduce this state-dependent impulsive neural networks system to a fix time impulsive neural networks system. Sufficient conditions for existence and global exponential stability of the equilibrium point as well as periodic solution are obtained by employing a suitable Lyapunov function, the Banach fixed point theorem and the Halanay-type impulsive differential inequality technique. Finally, two examples with numerical simulations to show the effectiveness of our theoretical results are illustrated.

Suggestions

Periodic solution for state-dependent impulsive shunting inhibitory CNNs with time-varying delays
Sayli, Mustafa; YILMAZ, ENES (2015-08-01)
In this paper, we consider existence and global exponential stability of periodic solution for state-dependent impulsive shunting inhibitory cellular neural networks with time-varying delays. By means of B-equivalence method, we reduce these state-dependent impulsive neural networks system to an equivalent fix time impulsive neural networks system. Further, by using Mawhin's continuation theorem of coincide degree theory and employing a suitable Lyapunov function some new sufficient conditions for existence...
Global exponential stability of neural networks with non-smooth and impact activations
Akhmet, Marat (2012-10-01)
In this paper, we consider a model of impulsive recurrent neural networks with piecewise constant argument. The dynamics are presented by differential equations with discontinuities such as impulses at fixed moments and piecewise constant argument of generalized type. Sufficient conditions ensuring the existence, uniqueness and global exponential stability of the equilibrium point are obtained. By employing Green's function we derive new result of existence of the periodic solution. The global exponential s...
Impulsive Hopfield-type neural network system with piecewise constant argument
Akhmet, Marat; Yılmaz, Elanur (2010-08-01)
In this paper we introduce an impulsive Hopfield-type neural network system with piecewise constant argument of generalized type. Sufficient conditions for the existence of the unique equilibrium are obtained. Existence and uniqueness of solutions of such systems are established. Stability criterion based on linear approximation is proposed. Some sufficient conditions for the existence and stability of periodic solutions are derived. An example with numerical simulations is given to illustrate our results.
Stability analysis of recurrent neural networks with piecewise constant argument of generalized type
Akhmet, Marat; Yılmaz, Elanur (2010-09-01)
In this paper, we apply the method of Lyapunov functions for differential equations with piecewise constant argument of generalized type to a model of recurrent neural networks (RNNs). The model involves both advanced and delayed arguments. Sufficient conditions are obtained for global exponential stability of the equilibrium point. Examples with numerical simulations are presented to illustrate the results.
Poisson Stability in Symmetrical Impulsive Shunting Inhibitory Cellular Neural Networks with Generalized Piecewise Constant Argument
Akhmet, Marat; Tleubergenova, Madina; Seilova, Roza; Nugayeva, Zakhira (2022-09-01)
In the paper, shunting inhibitory cellular neural networks with impulses and the generalized piecewise constant argument are under discussion. The main modeling novelty is that the impulsive part of the systems is symmetrical to the differential part. Moreover, the model depends not only on the continuous time, but also the generalized piecewise constant argument. The process is subdued to Poisson stable inputs, which cause the new type of recurrent signals. The method of included intervals, recently introd...
Citation Formats
M. Sayli and E. YILMAZ, “State-dependent impulsive Cohen-Grossberg neural networks with time-varying delays,” NEUROCOMPUTING, pp. 1375–1386, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/64411.