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: In this paper, a bifurcation diagram including an analytical Melnikov solution is presented for a canonical asymmetric cubic potential, and comparisons are made with recent results for the Holmes two-well oscillator.
79 citations
TL;DR: Using the upper and lower solutions method, a sufficient condition on parameters is given so that the coexistence equilibrium is globally asymptotically stable.
Abstract: In this paper, we consider a delayed diffusive Leslie–Gower predator–prey system with homogeneous Neumann boundary conditions. The stability/instability of the coexistence equilibrium and associated Hopf bifurcation are investigated by analyzing the characteristic equations. Furthermore, using the upper and lower solutions method, we give a sufficient condition on parameters so that the coexistence equilibrium is globally asymptotically stable.
79 citations
TL;DR: This paper reports on the stability analysis of one member of a dual-channel resonant DC-DC converter family confined to the buck configuration in symmetrical operation, and develops a bifurcation diagram showing the four possible states of the feedback loop.
Abstract: This paper reports on the stability analysis of one member of a dual-channel resonant DC-DC converter family. The study is confined to the buck configuration in symmetrical operation. The output voltage of the converter is controlled by a closed loop applying constant-frequency pulsewidth modulation. The dynamic analysis reveals that a bifurcation cascade develops as a result of increasing the loop gain. The trajectory of the variable-structure piecewise-linear nonlinear system pierces through the Poincare plane at the fixed point in state space when the loop gain is small. For stability criterion the positions of the characteristic multipliers of the Jacobian matrix belonging to the Poincare map function defined around the fixed point located in the Poincare plane is applied. In addition to the stability analysis, a bifurcation diagram is developed showing the four possible states of the feedback loop: the periodic, the quasi-periodic, the subharmonic, and the chaotic states. Simulation and test results verify the theory.
78 citations
TL;DR: It is proven that there exists a critical value of delay for the stability of virus prevalence and when the delay exceeds the critical value, the system loses its stability and a Hopf bifurcation occurs.
78 citations
01 Jul 2002
TL;DR: In this paper, the authors introduce an explicit multiparameter family of periodic structures with localized defects, which support linear defect modes and investigate the capture of an incident gap soliton by these defects.
Abstract: Gap solitons are localized nonlinear coherent states that have been shown both theoretically and experimentally to propagate in periodic structures. Although theory allows for their propagation at any speed v,0⩽v⩽c, they have been observed in experiments at speeds of approximately 50% of c. It is of scientific and technological interest to trap gap solitons. We first introduce an explicit multiparameter family of periodic structures with localized defects, which support linear defect modes. These linear defect modes are shown to persist into the nonlinear regime, as nonlinear defect modes. Using mathematical analysis and numerical simulations, we then investigate the capture of an incident gap soliton by these defects. The mechanism of capture of a gap soliton is resonant transfer of its energy to nonlinear defect modes. We introduce a useful bifurcation diagram from which information on the parameter regimes of gap-soliton capture, reflection, and transmission can be obtained by simple conservation of energy and resonant energy transfer principles.
78 citations