Results 141 to 150 of about 328 (171)
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Computation and Continuation of Homoclinic and Heteroclinic Orbits with Arclength Parameterization
SIAM Journal on Scientific Computing, 1997Summary: We study a numerical method for the computation and continuation of homoclinic and heteroclinic orbits based upon the arclength parametrization of the orbits. Unlike most other methods, this method utilizes the geometric structure of the homoclinic and heteroclinic orbits and does not require solving a boundary value problem (BVP) on an ...
Lixin Liu +2 more
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Power Spectrum of a Noisy System Close to a Heteroclinic Orbit
Journal of Statistical Physics, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Benjamin Lindner +2 more
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Approximating sequences for heteroclinic orbits
Mathematical Methods in the Applied Sciences, 1994AbstractIn this paper we construct two approximating sequences for heteroclinic solution to a scalar ODE. These sequences do not ‘intersect’ and bound a unique real solution from below and above, thus enabling us to estimate this solution with any accuracy.
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Interactive Initialization and Continuation of Homoclinic and Heteroclinic Orbits in MATLAB
ACM Transactions on Mathematical Software, 2012matcontis amatlabcontinuation package for the interactive numerical study of a range of parameterized nonlinear dynamical systems, in particular ODEs, that allows to compute curves of equilibria, limit points, Hopf points, limit cycles, flip, fold and torus bifurcation points of limit cycles.
Virginie De Witte +3 more
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On the heteroclinic orbit of the point vortex problem
Nonlinear Analysis: Theory, Methods & Applications, 1997The author studies the dynamics of a particular differential equation on \(\mathbb{C}^2\), that occurs in the study of the motion of 5 point vortices in the plane. A result on the existence of heteroclinic connections between steady state solutions is announced.
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Large heteroclinic orbits for some evolution equations
Nonlinear Analysis: Theory, Methods & Applications, 1988We deal with the existence of heteroclinic orbits for a semilinear elliptic equation with boundary conditions on an unbounded domain. In particular, we consider a problem like \[ -\Delta u+f(u)=0\quad in\quad S;\quad u=0\quad on\quad \partial S \] where S is a strip, \(S={\mathbb{R}}\times \Omega\) with \(\Omega \subset {\mathbb{R}}^ n\) a bounded ...
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Infinitely Many Heteroclinic Orbits of a Complex Lorenz System
International Journal of Bifurcation and Chaos, 2017The existence of heteroclinic orbits of a chaotic system is a difficult yet interesting mathematical problem. Nowadays, a rigorous analytical proof for the existence of a heteroclinic orbit can be carried out only for some special chaotic and hyperchaotic systems, and few results are known for the complex systems.
Haijun Wang, Xianyi Li
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Heteroclinic orbits in a spherically invariant system
Physica D: Nonlinear Phenomena, 1991Using numerical study, \textit{P. Friedrich} and \textit{H. Haken} dealt with steady state mode interactions for a convection problem in a spherical shell and revealed apparently chaotic trajectories which connected different equilibria of the system [see Phys. Rev. A 34, 2100-2120 (1986)]. These trajectories are suggestive of heteroclinic connections.
Armbruster, Dieter, Chossat, Pascal
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STOCHASTIC AVERAGING NEAR LONG HETEROCLINIC ORBITS
Stochastics and Dynamics, 2007We refine some of the bounds of [10]. There, we considered the effect of diffusive perturbations on a two-dimensional ODE with a heteroclinic cycle. We constructed corrector functions for asymptotically "glueing" together behavior of periodic orbits in the boundary layer near the heteroclinic cycle.
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Applying Lin's method to constructing heteroclinic orbits near the heteroclinic chain
Mathematical Methods in the Applied SciencesIn this paper, we apply Lin's method to study the existence of heteroclinic orbits near the degenerate heteroclinic chain under ‐dimensional periodic perturbations. The heteroclinic chain consists of two degenerate heteroclinic orbits and connected by three hyperbolic saddle points .
Bin Long, Yiying Yang
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