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: The main result of this paper indicates that the necessary condition for the creation of chaos in the resonator is intersection of the system steady state response with the homoclinic orbit.
58 citations
TL;DR: In this paper, a dynamic state-feedback control law is proposed to relocate two Hopf bifurcation points simultaneously, to any desired locations in n -dimensional nonlinear systems.
58 citations
TL;DR: In this paper, numerically obtained bounded solutions of the one-dimensional complex Ginzburg-Landau equation with a destabilizing cubic term and no stabilizing higher-order contributions are presented.
Abstract: We preent numerically obtained bounded solutions of the one-dimensional complex Ginzburg-Landau equation with a destabilizing cubic term and no stabilizing higher-order contributions. The boundedness results from competition between dispersion and nonlinear frequency renormalization. We find chaotic and also stationary and time-periodic states with spatial structure corresponding to a periodic array of pulses. An analytical description is presented. Possibly experimental results connected with the dispersive chaos found in binary-fluid mixtures can be explained.
58 citations
TL;DR: In this paper, the authors investigate analytically the effect on a period-doubling cascade of slowly sweeping the bifurcation parameter, by means of asymptotic calculations.
58 citations
TL;DR: This paper proposes a simple physical model using the modified van der Pol equation, which unfolds the generic synchronization behaviors of the latter kind and in which one may readily observe changes in the sychronization behaviors between the distinctive regimes as well.
Abstract: It has been known that a diffusive coupling between two limit cycle oscillations typically leads to the in-phase synchronization and also that it is the only stable state in the weak-coupling limit. Recently, however, it has been shown that the coupling of the same nature can result in the distinctive dephased synchronization when the limit cycles are close to the homoclinic bifurcation, which often occurs especially for the neuronal oscillators. In this paper we propose a simple physical model using the modified van der Pol equation, which unfolds the generic synchronization behaviors of the latter kind and in which one may readily observe changes in the sychronization behaviors between the distinctive regimes as well. The dephasing mechanism is analyzed both qualitatively and quantitatively in the weak-coupling limit. A general form of coupling is introduced and the synchronization behaviors over a wide range of the coupling parameters are explored to construct the phase diagram using the bifurcation analysis.
58 citations