Results 21 to 30 of about 5,108 (187)

Connected simple systems, transition matrices, and heteroclinic bifurcations [PDF]

Transactions of the American Mathematical Society, 1992
Given invariant sets A A , B B , and C C , and connecting orbits A → B A \to B and B → C B \to C , we state very general conditions under which they bifurcate to produce an A → C A \
McCord, Christopher, Mischaikow, Konstantin   +1 more
openaire   +2 more sources

Nonlinear stochastic dynamics research on a Lorenz system with white Gaussian noise based on a quasi‐potential approach

International Journal of Mechanical System Dynamics, Volume 3, Issue 1, Page 85-94, March 2023., 2023
Abstract Environmental noise can lead to complex stochastic dynamical behaviors in nonlinear systems. In this paper, a Lorenz system with the parameter region with two stable fixed points and a chaotic saddle subject to white Gaussian noise is investigated as an example.
Yong Huang
wiley   +1 more source

Cycling chaos: its creation, persistence and loss of stability in a model of nonlinear magnetoconvection [PDF]

, 1998
We examine a model system where attractors may consist of a heteroclinic cycle between chaotic sets; this ‘cycling chaos’ manifests itself as trajectories that spend increasingly long periods lingering near chaotic invariant sets interspersed with short ...
A.M. Rucklidge, Alexander, Ashwin, Ashwin, Ashwin, Ashwin, Barreto, Chow, Covas, Dellnitz, Field, Guckenheimer, Knobloch, Krupa, Matthews, Milnor, Milnor, Ott, Peter Ashwin, Platt, Press, Rucklidge, Rucklidge, Sigmund   +23 more
core   +3 more sources

Global Bifurcation Behaviors and Control in a Class of Bilateral MEMS Resonators

Fractal and Fractional, 2022
The investigation of global bifurcation behaviors the vibrating structures of micro-electromechanical systems (MEMS) has received substantial attention. This paper considers the vibrating system of a typical bilateral MEMS resonator containing fractional
Yijun Zhu, Huilin Shang
doaj   +1 more source

Analysis of the shearing instability in nonlinear convection and magnetoconvection [PDF]

, 1996
Numerical experiments on two-dimensional convection with or without a vertical magnetic field reveal a bewildering variety of periodic and aperiodic oscillations.
A M Rucklidge, Arnéodo A, Beyn W-J, Brownjohn D P, Brummell N, Champneys A R, Chandrasekhar S, Chui A Y K, Deardorff J W, Dellnitz M, Doedel E, Glendinning P, Glendinning P, Glendinning P, Glendinning P, Golubitsky M, Guckenheimer J, Howard L N, Hughes D W, Knobloch E, Krishnamurti R, Lythe G D, Massaguer J M, Matthews P C, Matthews P C, Moore D R, P C Matthews, Proctor M R E, Proctor M R E, Proctor M R E, Proctor M R E, Rucklidge A M, Rucklidge A M, Rucklidge A M, Rucklidge A M, Rucklidge A M, Rüdiger G, Shil'nikov A L, Sparrow C, Tabeling P, Weiss N O, Willis G E   +41 more
core   +1 more source

Bifurcations of Orbit and Inclination Flips Heteroclinic Loop with Nonhyperbolic Equilibria

The Scientific World Journal, 2014
The bifurcations of heteroclinic loop with one nonhyperbolic equilibrium and one hyperbolic saddle are considered, where the nonhyperbolic equilibrium is supposed to undergo a transcritical bifurcation; moreover, the heteroclinic loop has an orbit flip ...
Fengjie Geng, Junfang Zhao
doaj   +1 more source

Bifurcation analysis of a two-dimensional discrete Hindmarsh–Rose type model

Advances in Difference Equations, 2019
In this paper, bifurcation analysis of a discrete Hindmarsh–Rose model is carried out in the plane. This paper shows that the model undergoes a flip bifurcation, a Neimark–Sacker bifurcation, and 1:2 $1:2$ resonance which includes a pitchfork bifurcation,
Bo Li, Qizhi He
doaj   +1 more source

Initial-Sensitive Dynamical Behaviors of a Class of Geometrically Nonlinear Oscillators

Shock and Vibration, 2022
The vibrating system of a class of linkage-slider structure is considered, and its initial-sensitive dynamical behaviors such as safe jump, locking instability, and chaos are studied. First, static bifurcation of the dynamical system is discussed.
Bo Qin, Huilin Shang, Huimin Jiang
doaj   +1 more source

Dynamics of a Predator–Prey Model with the Additive Predation in Prey

Mathematics, 2022
In this paper, we consider a predator–prey model, in which the prey’s growth is affected by the additive predation of its potential predators. Due to the additive predation term in prey, the model may exhibit the cases of the strong Allee effect, weak ...
Dingyong Bai, Xiaoxuan Zhang
doaj   +1 more source

Some results on homoclinic and heteroclinic connections in planar systems [PDF]

, 2009
Consider a family of planar systems depending on two parameters $(n,b)$ and having at most one limit cycle. Assume that the limit cycle disappears at some homoclinic (or heteroclinic) connection when $\Phi(n,b)=0.$ We present a method that allows to ...
Andronov A A, Armengol Gasull, Boisseau B, Coll B, Dumortier F, Gil-Jun Han, Guckenheimer J, Hector Giacomini, Joan Torregrosa, Li C, Perko L M, Rozet I G, Rozet I G   +12 more
core   +4 more sources