Stability Analysis Of Neural Networks With Time Delays And Non-H(o|¨)lder Activation Functions

In signal,image processing,classification,associate memories,optimization, cryptogr-aphy and so on,Much effort has been made in the stability of neural networks,Due toneural networks’ potential applications in many areas,there has very popular in the studyof neural networks’ stability, All the results reported in the stability of neural networks areconcerned with Lipschitz activation functions,very little attention has been paid to theproblem of the stability for neural networks with inverse Lipschitz activation functions,benear inverse H(o|¨)lder activation functions.In this case, the stability of neural networks needsome special conditions,so the stability of neural networks which with inverse H(o|¨)lderactivation functions has the high value. The main works of this paper are as follows:To give a sufficient condition which ensures that the Cohen-Grossberg network withinverse H(o|¨)lder activation is globally exponentially stable is established.By applyingbrouwer degree properties and LMI approach,The existence and uniqueness of theequilibrium point has proofed,To provide suitable Lyapunov functional,a sufficientcondition which ensures that the Cohen-Grossberg network with inverse H(o|¨)lderactivation is globally exponentially stable is established.In view of the globally exponentially stability of the Cohen-Grossberg network, Byapplying the average dwell time approach and to provide suitable Lyapunov functional,asufficient condition which ensures that the switched Cohen-Grossberg networkwith inverse H(o|¨)lder activation is stable is established.To study the stability of the recurrent delayed Hopfield network with inverseH(o|¨)lder activation and Markovian jumping parameters,inquiry the existence anduniqueness of the equilibrium point, to provide suitable Lyapunov functional and the weakinfinitesimal operator, a sufficient condition which ensures that the recurrent delayedHopfield network with inverse H(o|¨)lder activation and Markovian jumping parametersstochastic exponentially stable is established.the conclution of this paper provide the newmethod and theoretical results.