Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3

Hopf bifurcation Related Publications

3 Frequency Domain Analysis for Hopf Bifurcation in a Delayed Competitive Web-site Model

Authors: Changjin Xu, Yusen Wu

Abstract:

In this paper, applying frequency domain approach, a delayed competitive web-site system is investigated. By choosing the parameter α as a bifurcation parameter, it is found that Hopf bifurcation occurs as the bifurcation parameter α passes a critical values. That is, a family of periodic solutions bifurcate from the equilibrium when the bifurcation parameter exceeds a critical value. Some numerical simulations are included to justify the theoretical analysis results. Finally, main conclusions are given.

Keywords: Stability, frequency domain, Nyquist criterion, Hopf bifurcation, Web-site system

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 897
2 Neuron Dynamics of Single-Compartment Traub Model for Hardware Implementations

Authors: J. C. Moctezuma, V. Breña-Medina, Jose Luis Nunez-Yanez and Joseph P. McGeehan

Abstract:

In this work we make a bifurcation analysis for a single compartment representation of Traub model, one of the most important conductance-based models. The analysis focus in two principal parameters: current and leakage conductance. Study of stable and unstable solutions are explored; also Hop-bifurcation and frequency interpretation when current varies is examined. This study allows having control of neuron dynamics and neuron response when these parameters change. Analysis like this is particularly important for several applications such as: tuning parameters in learning process, neuron excitability tests, measure bursting properties of the neuron, etc. Finally, a hardware implementation results were developed to corroborate these results.

Keywords: Traub model, Pinsky-Rinzel model, single-compartment models, bifurcation analysis, Hopf bifurcation, neuron modeling

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 813
1 Bifurcations for a FitzHugh-Nagumo Model with Time Delays

Authors: Changjin Xu, Peiluan Li

Abstract:

In this paper, a FitzHugh-Nagumo model with time delays is investigated. The linear stability of the equilibrium and the existence of Hopf bifurcation with delay τ is investigated. By applying Nyquist criterion, the length of delay is estimated for which stability continues to hold. Numerical simulations for justifying the theoretical results are illustrated. Finally, main conclusions are given.

Keywords: Stability, Time Delay, FitzHugh-Nagumo model, Hopf bifurcation

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1311