High-Order Melnikov Method for Time-Periodic Equations
Advanced Nonlinear Studies, 2017 This paper discusses a high-order Melnikov method for periodically perturbed equations. We introduce a new method to compute Mk(t0){M_{k}(t_{0})} for all k≥0{k\geq 0}, among which M0(t0){M_{0}(t_{0})} is the traditional Melnikov function, and M1(t0 ...
Chen Fengjuan, Wang Qiudong
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Transversal heteroclinic and homoclinic orbits in singular perturbation problems
Journal of Differential Equations, 1991 In this paper we give a geometric construction of heteroclinic and homoclinic orbits for singularly perturbed differential equations. By using methods from invariant manifold theory we show that transversal intersection of stable and unstable manifolds ...
Peter Szmolyan
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Homoclinic chaos in the dynamics of a general Bianchi type-IX model [PDF]
, 2002 The dynamics of a general Bianchi IX model with three scale factors is examined. The matter content of the model is assumed to be comoving dust plus a positive cosmological constant. The model presents a critical point of saddle-center-center type in the
H. P. de Oliveira +3 more
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The transversal homoclinic solutions and chaos for stochastic ordinary differential equations
Journal of Mathematical Analysis and Applications, 2014 Guang-Ping Luo, Juan Liang, C. Zhu
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Homoclinic orbits in Hamiltonian systems
, 1976 The object of this paper is to study the orbit structure of a Hamiltonian system in a neighborhood of a trajectory which is doubly asymptotic to an equilibrium solution, i.e., an orbit which lies in the intersection of the stable and unstable manifolds ...
R. Devaney
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Non-transversal intersection of the free and fixed boundary in the mean-field theory of superconductivity [PDF]
Interfaces and free boundaries (Print), 2018 Non-transversal intersection of the free and fixed boundary is shown to hold and a classification of blow-up solutions is given for obstacle problems generated by fully nonlinear uniformly elliptic operators in two dimensions which appear in the mean ...
E. Indrei
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Multidimensional Diffeomorphisms with Stable Periodic Points
Vestnik St Petersburg University Mathematics, 2019 Diffeomorphisms of a multidimensional space into itself with a hyperbolic fixed point are discussed in this paper. It is assumed that at the intersection of stable and unstable manifolds, there are points that are different from the hyperbolic point ...
E. V. Vasil'eva
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Transversal intersection of monomial ideals [PDF]
Proceedings - Mathematical Sciences, 2017 In this paper, we prove conditions for transversal intersection of monomial ideals and derive a simplicial characterization of this phenomenon.
Joydip Saha +2 more
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Analytical study of the Lorenz system: Existence of infinitely many periodic orbits and their topological characterization. [PDF]
Proc Natl Acad Sci U S A, 2023 Pinsky T.
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Pseudo-nullclines enable the analysis and prediction of signaling model dynamics. [PDF]
Front Cell Dev Biol, 2023 Marrone JI, Sepulchre JA, Ventura AC.
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