Results 21 to 30 of about 648 (183)
Beltrami fields and knotted vortex structures in incompressible fluid flows
Bulletin of the London Mathematical Society, Volume 55, Issue 3, Page 1059-1103, June 2023., 2023 Abstract This paper gives a survey on recent results about the existence of knotted vortex structures in incompressible fluids. This includes the proof of Lord Kelvin's conjecture on the existence of knotted vortex tubes in steady Euler flows and a new probabilistic approach to address Arnold's speculation that typical Beltrami fields should exhibit ...
Alberto Enciso, Daniel Peralta‐Salas
wiley +1 more source
Topology of optimal flows with collective dynamics on closed orientable surfaces
Pracì Mìžnarodnogo Geometričnogo Centru, 2020 We consider flows on a closed surface with one or more heteroclinic cycles that divide the surface into two regions. One of the region has gradient dynamics, like Morse fields.
Alexandr Olegovich Prishlyak +1 more
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Control of noisy heteroclinic cycles
Physica D: Nonlinear Phenomena, 1994 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Brianno Coller +2 more
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Singular Orbits and Dynamics at Infinity of a Conjugate Lorenz-Like System
Mathematical Modelling and Analysis, 2015 A conjugate Lorenz-like system which includes only two quadratic nonlinearities is proposed in this paper. Some basic properties of this system, such as the distribution of its equilibria and their stabilities, the Lyapunov exponents, the bifurcations ...
Fengjie Geng, Xianyi Li
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Stability of quasi-simple heteroclinic cycles [PDF]
Dynamical Systems, 2018 The stability of heteroclinic cycles may be obtained from the value of the local stability index along each connection of the cycle. We establish a way of calculating the local stability index for quasi-simple cycles: cycles whose connections are 1-dimensional and contained in flow-invariant spaces of equal dimension.
Liliana Garrido-da-Silva +1 more
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Heteroclinic cycles between unstable attractors [PDF]
Nonlinearity, 2008 We consider networks of pulse coupled linear oscillators with non-zero delay where the coupling between the oscillators is given by the Mirollo-Strogatz function. We prove the existence of heteroclinic cycles between unstable attractors for a network of four oscillators and for an open set of parameter values.
Broer, Henk +2 more
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Limit Cycles Bifurcated from Some Z4-Equivariant Quintic Near-Hamiltonian Systems
Abstract and Applied Analysis, 2014 We study the number and distribution of limit cycles of some planar Z4-equivariant quintic near-Hamiltonian systems. By the theories of Hopf and heteroclinic bifurcation, it is proved that the perturbed system can have 24 limit cycles with some new ...
Simin Qu +3 more
doaj +1 more source
Some examples for stable and historic behavior in replicator equations
Examples and Counterexamples, 2022 The evolutionary dynamics of zero-sum and non zero-sum games under replicator equations could be drastically different from each other. In zero-sum games, heteroclinic cycles naturally occur whenever the species of the population supersede each other in ...
Mansoor Saburov
doaj +1 more source
Heteroclinic Cycles in a Competitive Network
International Journal of Bifurcation and Chaos, 2017 The competitive threshold linear networks have been recently developed and are typical examples of nonsmooth systems that can be easily constructed. Due to their flexibility for manipulation, they are used in several applications, but their dynamics (both local and global) are not completely understood.
Ulises Chialva, Walter Reartes
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Effect of Axial and Radial Flow on the Hydrodynamics in a Taylor Reactor
Fluids, 2022 This paper investigates the impact of combined axial through flow and radial mass flux on Taylor–Couette flow in a counter-rotating configuration, in which different branches of nontrivial solutions appear via Hopf bifurcations.
Sebastian A. Altmeyer
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