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Yayın Equilibrium and stability analysis of delayed neural networks under parameter uncertainties(Elsevier Science Inc, 2012-02-15) Faydasıçok, Özlem; Arik, SabriThis paper proposes new results for the existence, uniqueness and global asymptotic stability of the equilibrium point for neural networks with multiple time delays under parameter uncertainties. By using Lyapunov stability theorem and applying homeomorphism mapping theorem, new delay-independent stability criteria are obtained. The obtained results are in terms of network parameters of the neural system only and therefore they can be easily checked. We also present some illustrative numerical examples to demonstrate that our result are new and improve corresponding results derived in the previous literature.Yayın A new robust stability criterion for dynamical neural networks with multiple time delays(Elsevier Science BV, 2013-01-01) Faydasıçok, Özlem; Arik, SabriThis paper investigates the problem of the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with multiple time delays and parameter uncertainties. Under the assumption that the activation functions are globally Lipschitz continuous, we derive a new criterion for the robust stability of a class of delayed neural networks by utilizing the Lyapunov stability theorems and the Homomorphic mapping theorem. Different from those previously published conditions in the recent literature, the robust stability result presented in this paper not only establishes a time-independent relationship between the network parameters of the neural network, but also takes into account the number the neurons of the designed neural system. Some illustrative numerical examples are also given to make a detailed comparison between our result and the previously published corresponding results. This comparison proves that our result is new and can be considered an alternative condition to those of the previously reported robust stability results.Yayın Further analysis of global robust stability of neural networks with multiple time delays(Pergamon-Elsevier Science Ltd, 2012-04) Faydasıçok, Özlem; Arik, SabriThis paper deals with the problem of the global robust asymptotic stability of the class of dynamical neural networks with multiple time delays. We propose a new alternative sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point under parameter uncertainties of the neural system. We first prove the existence and uniqueness of the equilibrium point by using the Homomorphic mapping theorem. Then, by employing a new Lyapunov functional, the Lyapunov stability theorem is used to establish the sufficient condition for the asymptotic stability of the equilibrium point. The obtained condition is independent of time delays and relies on the network parameters of the neural system only. Therefore, the equilibrium and stability properties of the delayed neural network can be easily checked. We also make a detailed comparison between our result and the previous corresponding results derived in the previous literature. This comparison proves that our result is new and improves some of the previously reported robust stability results. Some illustrative numerical examples are given to show the applicability and advantages of our result.Yayın New robust stability results for bidirectional associative memory neural networks with multiple time delays(Elsevier Science Inc, 2012-08-01) Senan, Sibel; Arik, Sabri; Liu, DerongIn this paper, the robust stability problem is investigated for a class of bidirectional associative memory (BAM) neural networks with multiple time delays. By employing suitable Lyapunov functionals and using the upper bound norm for the interconnection matrices of the neural network system, some novel sufficient conditions ensuring the existence, uniqueness and global robust stability of the equilibrium point are derived. The obtained results impose constraint conditions on the system parameters of neural network independent of the delay parameters. Some numerical examples and simulation results are given to demonstrate the applicability and effectiveness of our results, and to compare the results with previous robust stability results derived in the literature.Yayın A new condition for robust stability of uncertain neural networks with time delays(Elsevier Science BV, 2014-03-27) Arik, SabriThis paper is concerned with the global asymptotic stability problem of dynamical neural networks with multiple time delays under parameter uncertainties. First carrying out an analysis of existence and uniqueness of the equilibrium point by means of the Homeomorphism theory, and then, studying the global asymptotic stability of the equilibrium point by constructing a suitable Lyapunov functional, we derive a new global robust stability criterion for the class of delayed neural networks with respect to the Lipschitz activation functions. The result obtained establishes a relationship between the neural network parameters only and it is independent of the time delay parameters. It is shown that the established stability condition generalizes some existing ones and it can be considered to an alternative result to some other corresponding results derived in previous literature. We also give some comparative numerical examples to demonstrate the validity and effectiveness of our proposed result.Yayın An improved robust stability result for uncertain neural networks with multiple time delays(Pergamon-Elsevier Science Ltd, 2014-06) Arik, SabriThis paper proposes a new alternative sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of delayed neural networks under the parameter uncertainties of the neural system. The existence and uniqueness of the equilibrium point is proved by using the Homomorphic mapping theorem. The asymptotic stability of the equilibrium point is established by employing the Lyapunov stability theorems. The obtained robust stability condition establishes a new relationship between the network parameters of the system. We compare our stability result with the previous corresponding robust stability results derived in the past literature. Some comparative numerical examples together with some simulation results are also given to show the applicability and advantages of our result.
