Results 41 to 50 of about 8,177 (202)

Kuramoto Phase Model with Inertia: Bifurcations Leading to the Loss of Synchrony and to the Emergence of Chaos

Моделирование и анализ информационных систем, 2015
We consider a finite-dimensional model of phase oscillators with inertia in the case of star configuration of coupling. The system of equations is reduced to a nonlinearly coupled system of pendulum equations.
V. N. Belykh, M. I. Bolotov, G. V. Osipov   +2 more
doaj   +1 more source

Homoclinic bifurcations in low-Prandtl-number Rayleigh-B\'{e}nard convection with uniform rotation

, 2013
We present results of direct numerical simulations on homoclinic gluing and ungluing bifurcations in low-Prandtl-number ($ 0 \leq Pr \leq 0.025 $) Rayleigh-B\'{e}nard system rotating slowly and uniformly about a vertical axis.
Kumar, K., Maity, P., Pal, P.
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Vibration of the Duffing Oscillator: Effect of Fractional Damping

Shock and Vibration, 2007
We have applied the Melnikov criterion to examine a global homoclinic bifurcation and transition to chaos in a case of the Duffing system with nonlinear fractional damping and external excitation.
Marek Borowiec, Grzegorz Litak, Arkadiusz Syta   +2 more
doaj   +1 more source

Periodic Solutions and Homoclinic Bifurcations of Two Predator-Prey Systems with Nonmonotonic Functional Response and Impulsive Harvesting

Journal of Applied Mathematics, 2014
Two predator-prey models with nonmonotonic functional response and state-dependent impulsive harvesting are formulated and analyzed. By using the geometry theory of semicontinuous dynamic system, we obtain the existence, uniqueness, and stability of the ...
Mingzhan Huang, Xinyu Song
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Dynamics of Unilateral and Bilateral Control Systems with State Feedback for Renewable Resource Management

Complexity, 2020
In this paper, mathematical models for the management of biological resources based on a given predator-prey relationship are proposed, and two types of control strategies, unilateral and bilateral control with impulsive state feedback, are studied.
Mingzhan Huang, Shouzong Liu, Xinyu Song, Lansun Chen   +3 more
doaj   +1 more source

Invariant manifolds of the Bonhoeffer-van der Pol oscillator

, 2010
The stable and unstable manifolds of a saddle fixed point (SFP) of the Bonhoeffer-van der Pol oscillator are numerically studied. A correspondence between the existence of homoclinic tangencies (whic are related to the creation or destruction of Smale ...
Benítez, R., Bolós, V. J.
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Symbolic Toolkit for Chaos Explorations [PDF]

, 2013
New computational technique based on the symbolic description utilizing kneading invariants is used for explorations of parametric chaos in a two exemplary systems with the Lorenz attractor: a normal model from mathematics, and a laser model from ...
A Shilnikov, A Shilnikov, A Shilnikov, A Vladimirov, AL Shilnikov, E. Lorenz, EN Lorenz, F Fernández-Sánchez, H. Haken, J Milnor, J Moloney, J. Guckenheimer, J.A.C. Gallas, JL Kaplan, L Shilnikov, L Shilnikov, L Shilnikov, L Shilnikov, L.P. Shilnikov, P. Gaspard, P. Glendinning, R Barrio, R. Barrio, R. Barrio, S. Gonchenko, T. Shimizu, U. Hubner, V Afraimovich, V. Afraimovich, V. Bykov, V.V. Bykov, W. Forysiak   +31 more
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Bifurcations of planar sliding homoclinics [PDF]

Mathematical Problems in Engineering, 2006
We study bifurcations from sliding homoclinic solutions to bounded solutions on ℝ for certain discontinuous planar systems under periodic perturbations. Sufficient conditions are derived for such perturbation problems.
Awrejcewicz, Jan, Fečkan, Michal, Olejnik, Pawel   +2 more
openaire   +1 more source

Bifurcation diagrams for singularly perturbed system

Electronic Journal of Qualitative Theory of Differential Equations, 2012
We consider a singularly perturbed system where the fast dynamic of the unperturbed problem exhibits a trajectory homoclinic to a critical point.
Matteo Franca
doaj   +1 more source

Kneadings, Symbolic Dynamics and Painting Lorenz Chaos. A Tutorial

, 2012
A new computational technique based on the symbolic description utilizing kneading invariants is proposed and verified for explorations of dynamical and parametric chaos in a few exemplary systems with the Lorenz attractor.
Abad A., Afraimovich V., Afraimovich V., ANDREY SHILNIKOV, Barrio R., Barrio R., Bykov V. V., Glendinning P., Gonchenko S. V., Hubner U., LEONID SHILNIKOV, Malkin M., ROBERTO BARRIO, Roshchin N., Rychlic M., Shilnikov A., Shilnikov L., Shilnikov L., Shilnikov L., Shilnikov L. P.   +19 more
core   +1 more source