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This paper considers the stability and Hopf bifurcation for a class of neural network model. Regard the delay ????as a parameter, this paper discussed the range of stability of an equilibrium point when0???????? and the conditions under which the system has a Hopf bifurcation can be obtained in this paper.
Using techniques developed by Kuznetsov to discrete-time systems, we study the stability of the equilibrium and Neimark — Sacker bifurcation (also called Hopf bifurcation for map) of a tri-neural network system. The theoretical analyses are verified by numerical simulations. Our results have potential applications in neural networks.
In this paper the bifurcation behavior of a TCP fluid model of Internet congestion control system is investigated. The parameter condition that the Hopf bifurcation occurs is deduced. The sufficient condition under which an impulsive system is asymptotically stable is present. An impulsive controller is proposed for controlling bifurcation in this system. Simulation results demonstrate that the complex...
In this paper, a class of neutral neural networks with delays is considered where the time delays are regarded as parameters. The linear stability of the model is studied by analyzing the distribution of the roots of the characteristic equation. It is found that Hopf bifurcation also occurs when some delays pass through a sequence of critical value.
The van der Pol equation with different discrete-time delay is analyzed. The resonant codimension-two bifurcation can be found, at which the transcendental characteristic equation possesses two pairs of pure imaginary roots, plusmniomega1, plusmn iomega2 with omega1 : omega2 = m:n, where m and n are positive integers. Some numerical simulation examples for justifying the theoretical analysis are also...
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