Topic
Bifurcation diagram
About: Bifurcation diagram is a research topic. Over the lifetime, 8379 publications have been published within this topic receiving 139664 citations.
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TL;DR: Results are provided here about the stability and bifurcation of periodic solutions for a (neural) network with n elements where delays between adjacent units and external inputs are included.
Abstract: Results are provided here about the stability and bifurcation of periodic solutions for a (neural) network with n elements where delays between adjacent units and external inputs are included. The particular cases n=2 and n=3 are discussed in details, to explicitly illustrate the role of the delays in the corresponding bifurcation sets and the stability properties, like a Hopf bifurcation, a pitchfork bifurcation, and a Bogdanov–Takens bifurcation.
52 citations
TL;DR: The bifurcation diagram of the BR equation predicts the region where instantaneous perturbations, such as brief current pulses, can send the stable repetitive rhythmic state into the stable steady state.
52 citations
TL;DR: A new 3-D chaotic system having only one stable equilibrium that has a state variable related with the freedom of offset boosting and the anti-synchronization of the system via an adaptive control is introduced.
Abstract: Recent evidences suggest that complex behavior such as chaos can be observed in a nonlinear system with stable equilibria. However, few studies have investigated chaotic systems with only one stable equilibrium. This paper introduces a new 3-D chaotic system having only one stable equilibrium. Dynamics of the new system are discovered by using phase portraits, basin of attraction, bifurcation diagram, and maximal Lyapunov exponents. It is interesting that the system has a state variable related with the freedom of offset boosting. In addition, we have investigated the anti-synchronization of the system via an adaptive control. Furthermore, the feasibility of the system is also discussed through presenting its electronic circuit implementation.
52 citations
TL;DR: A five-variable electron-hole model for a quantum-dot (QD) laser subject to optical feedback is studied and an analytical approximation for this critical feedback rate is derived proportional to the damping rate of the relaxation oscillations (ROs) and inversely proportional toThe linewidth enhancement factor.
Abstract: We study a five-variable electron-hole model for a quantum-dot (QD) laser subject to optical feedback. The model includes microscopically computed Coulomb scattering rates. We consider the case of a low linewidth enhancement factor and a short external cavity. We determine the bifurcation diagram of the first three external cavity modes and analyze their bifurcations. The first Hopf bifurcation marks the critical feedback rate below which the laser is stable. We derive an analytical approximation for this critical feedback rate that is proportional to the damping rate of the relaxation oscillations (ROs) and inversely proportional to the linewidth enhancement factor. The damping rate is described in terms of the carrier lifetimes. They depend on the specific band structure of the QD device and they are computed numerically.
52 citations
TL;DR: In this article, a general class of first-order nonlinear delay-differential equations (DDEs) with reflectional symmetry is considered, and the bifurcations of the trivial equilibrium under some generic conditions on the Taylor coefficients of the DDE are analyzed.
51 citations