Results 251 to 260 of about 1,245,923 (288)

Bifurcation scenarios for bubbling transition

Physical Review E, 2003
Dynamical systems with chaos on an invariant submanifold can exhibit a type of behavior called bubbling, whereby a small random or fixed perturbation to the system induces intermittent bursting. The bifurcation to bubbling occurs when a periodic orbit embedded in the chaotic attractor in the invariant manifold becomes unstable to perturbations ...
Aleksey V, Zimin, Brian R, Hunt, Edward, Ott   +2 more
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Basic structures of the Shilnikov homoclinic bifurcation scenario

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2005
We find numerically small scale basic structures of homoclinic bifurcation curves in the parameter space of the Chua circuit. The distribution of these basic structures in the parameter space and their geometrical properties constitute a complete homoclinic bifurcation scenario of this system.
Medrano-T., Rene O., Baptista, Murilo S., Caldas, Iberê L.   +2 more
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Bifurcation scenarios and quasiperiodicity in coupled maps

Physica A: Statistical Mechanics and its Applications, 1997
Abstract The appearance of coherent structures in a model of two coupled logistic maps is studied. Analytical results for the existence of multiple attractors and transitions from periodic to quasiperiodic motion are presented. The theoretical prediction for the Hopf radius agrees well with computer experiment throughout the quasiperiodic region.
Karl E. Kürten, Grégoire Nicolis
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Nonautonomous bifurcation scenarios in SIR models

Mathematical Methods in the Applied Sciences, 2015
The standard obstacles in developing a bifurcation theory for nonautonomous differential equations are the lack of steady‐state equilibria and the insignificance of eigenvalues in stability investigations. For this reason, various techniques have been proposed to specify changes in the qualitative behavior of time‐dependent dynamical systems.
Kloeden, P. E., Pötzsche, C.
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A Turing–Hopf Bifurcation Scenario for Pattern Formation on Growing Domains

Bulletin of Mathematical Biology, 2016
In this paper, we study the emergence of different patterns that are formed on both static and growing domains and their bifurcation structure. One of these is the so-called Turing-Hopf morphogenetic mechanism. The reactive part we consider is of FitzHugh-Nagumo type.
Castillo, Jorge A., Sánchez-Garduño, Faustino, Padilla, Pablo   +2 more
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A scenario for torus T2 destruction via a global bifurcation

Chaos, Solitons & Fractals, 2009
We show a scenario of a two-frequency torus breakdown, in which a global bifurcation occurs due to the collision of a quasi-periodic torus T 2 with saddle points, creating a heteroclinic saddle connection. We analyze the geometry of this torus-saddle collision by showing the local dynamics and the invariant manifolds (global dynamics) of the saddle ...
Pereira, Tiago, Baptista, Murilo da Silva, Reyes, Marcelo Bussotti, Caldas, Ibere Luiz, Sartorelli, José Carlos, Kurths, Jürgen (Prof. Dr.)   +5 more
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From Order to Chaos: Bifurcation Scenarios (Part II)

2014
According to the Ruelle–Takens–Newhouse scenario, the transition from quasiperiodicity to chaos occurs after the third frequency birth, when Lyapunov-unstable chaotic trajectories appear on a three-dimensional torus. However, the study of particular dynamical systems has shown that the appearance of chaos following the destruction of two-frequency ...
Vadim S. Anishchenko, Tatyana E. Vadivasova, Galina I. Strelkova   +2 more
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BIFURCATION SCENARIO OF A THREE-DIMENSIONAL VAN DER POL OSCILLATOR

International Journal of Bifurcation and Chaos, 1993
Nonlinear self-excited oscillations are usually investigated for two-dimensional models. We extend the simplest and best known of these models, the van der Pol oscillator, to a three-dimensional one and study its dynamical behaviour by methods of bifurcation analysis. We find cusps and other local codimension 2 bifurcations. A homoclinic (i.e. global)
Sünner, T., Sauermann, H.
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PERIOD-DOUBLING SCENARIO WITHOUT FLIP BIFURCATIONS IN A ONE-DIMENSIONAL MAP

International Journal of Bifurcation and Chaos, 2005
In this work a one-dimensional piecewise-smooth dynamical system, representing a Poincaré return map for dynamical systems of the Lorenz type, is investigated. The system shows a bifurcation scenario similar to the classical period-doubling one, but which is influenced by so-called border collision phenomena and denoted as border collision period ...
Viktor Avrutin, Michael Schanz
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Bifurcation scenarios for chirped mode locking in a semiconductor laser

Physical Review E
Using a delay differential equation model for a two-section semiconductor laser, we have found a new bifurcation scenario leading to stable mode-locked operation with normal dispersion properties of the light travel. The pulse profile is asymmetric, with a slower leading edge and a negative chirp.
G. S. Zhuravlev, A. V. Kovalev, A. E. Romanov, E. A. Viktorov   +3 more
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