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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 article, the authors consider the problem where $W$ invades the $(U,V)$ system in the three species Lotka-Volterra competition-diffusion model.
Abstract: We consider the problem where $W$ invades the $(U,V)$ system in the three species Lotka-Volterra competition-diffusion model. Numerical simulation indicates that the presence of $W$ can dramatically change the competitive interaction between $U$ and $V$ in some parameter range if the invading $W$ is not too small. We also construct exact travelling wave solutions with non-trivial three components and track the bifurcation branches of these solutions by AUTO.

39 citations

Journal ArticleDOI
TL;DR: In this paper, the authors considered the transverse stability of a pair of symmetrically coupled, identical Rossler systems and showed that desynchronization is associated with different orbits undergoing transverse pitchfork or period-doubling bifurcations.

39 citations

Journal ArticleDOI
TL;DR: In this paper, the bifurcation diagram of a laser with saturable absorber in the low and medium intensity regimes was investigated and the linear stability of the stationary solutions corresponding to these regimes was studied.
Abstract: We investigate the bifurcation diagram of a laser with saturable absorber in the low and medium intensity regimes The linear stability of the stationary solutions corresponding to these regimes is studied In the low intensity domain, a Hopf bifurcation point is determined from which a time-periodic solution emerges This solution is contructed and its stability is analyzed in the vicinity of the bifurcation point It is shown that this time-periodic solution is stable in a finite domain of the parameter space

39 citations

Journal ArticleDOI
Abstract: The nonlinear dynamics of a differential system describing the motion of a vehicle driven by a pilot is examined. In a first step, the stability of the system near the critical speed is analyzed by the bifurcation method in order to characterize its behavior after a loss of stability. It is shown that a Hopf bifurcation takes place, the stability of limit cycles depending mainly on the vehicle and pilot model parameters. In a second step, the front wheels of the vehicle are assumed to be subjected to a periodic disturbance. Chaotic and hyperchaotic motions are found to occur for some range of the speed parameter. Numerical simulations, such as bifurcation diagrams, Poincare maps, Fourier spectrums, projection of trajectories, and Lyapunov exponents are used to establish the existence of chaotic attractors. Multiple attractors may coexist for some values of the speed, and basins of attraction for such attractors are shown to have fractal geometries.

39 citations

Journal ArticleDOI
TL;DR: In this article, the authors discuss voltage collapse indices with the help of bifurcation theory and identify a well-behaved eigenvalue as a function of load increase.

39 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023122
2022326
2021187
2020195
2019166
2018220