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Exploring Limit Cycles of Differential Equations through Information Geometry Unveils the Solution to Hilbert's 16th Problem. [PDF]
Entropy (Basel)da Silva VB, Vieira JP, Leonel ED.
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Coexistence and extinction in flow-kick systems: An invasion growth rate approach. [PDF]
J Math BiolSchreiber SJ.
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Nonreciprocal synchronization in embryonic oscillator ensembles
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Applied Mathematics and Optimization, 1997
A heteroclinic cycle in a dynamical system is given by a finite cyclic sequence of trajectories each connecting two fixed points. Robustness means that a cycle nearby still exists after perturbing the system in a particular admissible way. Here, one allows for a stable state with high symmetry to lose its stability and some of its symmetry.
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A heteroclinic cycle in a dynamical system is given by a finite cyclic sequence of trajectories each connecting two fixed points. Robustness means that a cycle nearby still exists after perturbing the system in a particular admissible way. Here, one allows for a stable state with high symmetry to lose its stability and some of its symmetry.
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Structurally stable heteroclinic cycles
Mathematical Proceedings of the Cambridge Philosophical Society, 1988This paper describes a previously undocumented phenomenon in dynamical systems theory; namely, the occurrence of heteroclinic cycles that are structurally stable within the space of Cr vector fields equivariant with respect to a symmetry group. In the space X(M) of Cr vector fields on a manifold M, there is a residual set of vector fields having no ...
Guckenheimer, John, Holmes, Philip
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Homoclinic and Heteroclinic Bifurcations Close to a Twisted Heteroclinic Cycle
International Journal of Bifurcation and Chaos, 1998We study the interaction of a transcritical (or saddle-node) bifurcation with a codimension-0/codimension-2 heteroclinic cycle close to (but away from) the local bifurcation point. The study is motivated by numerical observations on the traveling wave ODE of a reaction–diffusion equation.
Zimmermann, Martín G. +1 more
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Heteroclinic cycles and wreath product symmetries
Dynamics and Stability of Systems, 2000We consider the existence and stability of heteroclinic cycles arising by local bifurcation in dynamical systems with wreath product symmetry = Z 2 G, where Z 2 acts by - 1 on R and G is a transitive subgroup of the permutation group S N (thus G has degree N). The group acts absolutely irreducibly on R N .
ANA PAULA S. DIAS +2 more
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Izvestiya, Physics of the Solid Earth, 2020
Heteroclinic cycle is an invariant of a dynamical system comprised of steady states (or more general invariant subsets) and heteroclinic trajectories. The behavior of a dynamical system with a heteroclinic cycle is intermittent: a typical trajectory stays for a long time close to a steady state while the transitions between the states occur much faster.
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Heteroclinic cycle is an invariant of a dynamical system comprised of steady states (or more general invariant subsets) and heteroclinic trajectories. The behavior of a dynamical system with a heteroclinic cycle is intermittent: a typical trajectory stays for a long time close to a steady state while the transitions between the states occur much faster.
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