Bifurcation analysis in a two-neuron system with different time delays
نویسنده
چکیده
In this paper, we consider a two-neuron system with time-delayed connections between neurons. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulation results are given to support the theoretical predictions. Finally, main conclusions are given. Keywords—Two-neuron system; Delay; Stability; Hopf bifurcation.
منابع مشابه
Bifurcation Analysis of a Simplified BAM Neural Network Model with Time Delays
In this paper, a five-neuron bidirectional associative memory (BAM) neural network with two time delays is studied. Since the study of Hopf bifurcation is very important for the design and application of BAM neural networks, we investigate that Hopf bifurcation occurs and a family of periodic solutions appear when the sum of two delays passes through a critical value.
متن کاملGlobal Hopf Bifurcation Analysis of a Neuron Network Model with Time Delays
For a two-neuron network with self-connection and time delays, we carry out stability and bifurcation analysis. We establish that a Hopf bifurcation occurs when the total delay passes a sequence of critical values. The stability and direction of the local Hopf bifurcation are determined using the normal form method and center manifold theorem. To show that periodic solutions exist away from the...
متن کاملBifurcation analysis for a discrete-time Hopfield neural network of two neurons with two delays
In this paper, a bifurcation analysis is undertaken for a discrete-time Hopfield neural network of two neurons with two different delays and self-connections. Conditions ensuring the asymptotic stability of the null solution are found, with respect to two characteristic parameters of the system. It is shown that for certain values of these parameters, fold or Neimark-Sacker bifurcations occur, ...
متن کاملVibration and Bifurcation Analysis of a Nonlinear Damped Mass Grounded System
In this paper, vibrations and bifurcation of a damped system consists of a mass grounded by linear and nonlinear springs and a nonlinear damper is studied. Nonlinear equation of motion is derived using Newton’s equations. Approximate analytical solutions are obtained using multiple time scales (MTS) method. For free vibration, the approximate analytical results are compared with the numerical i...
متن کاملStability and Hopf bifurcation analysis on a four-neuron BAM neural network with time delays
In this Letter, a four-neuron BAM neural network with four time delays is considered, where the time delays are regarded as parameters. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs when these delays pass through a sequence of critical value. A formula for determini...
متن کامل