Results 101 to 110 of about 8,022 (205)

Periodic or homoclinic orbit bifurcated from a heteroclinic loop for high-dimensional systems

Open Mathematics
Consider an autonomous ordinary differential equation in Rn{{\mathbb{R}}}^{n}, which has a heteroclinic loop. Assume that the heteroclinic loop consists of two degenerate heteroclinic orbits γ1{\gamma }_{1}, γ2{\gamma }_{2} and two saddle points with ...
Long Bin, Yang Yiying
doaj   +1 more source

Essential hyperbolicity and homoclinic bifurcations: a dichotomy phenomenon/mechanism for diffeomorphisms

, 2010
We prove that any diffeomorphism of a compact manifold can be approximated in topology C1 by another diffeomorphism exhibiting a homoclinic bifurcation (a homoclinic tangency or a heterodimensional cycle) or by one which is essentially hyperbolic (it has
Crovisier, Sylvain, Pujals, Enrique R.
core   +1 more source

The Homoclinic Orbits in the Liénard Plane

Journal of Mathematical Analysis and Applications, 1995
In reply to a question, posed by Roberto Conti, concerning the stability properties of the origin to a pseudolinear system in \(\mathbb{R}^ 2\), the situation is clarified for the well-known Liénard system. The notion of the maximal elliptic sector is shown to play an important role with respect to a zero solution to be a positive global (weak ...
openaire   +2 more sources

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.
europepmc   +1 more source

Encryption of Color Images Based on Chaotic Attractors Generated by ODE Systems Containing Module Nonlinearities

Journal of Optimization, Differential Equations and Their Applications
The main objective of this work is to construct an algorithm for modeling chaotic attractors using special neural ODEs with antisymmetric matrices (antisymmetric neural ODEs) and modular power nonlinearities.
Vasiliy Ye. Belozyorov, Natalia A. Guk, Danylo I. Yehoshkin   +2 more
doaj   +1 more source

Tightening Poincaré–Bendixson theory after counting separately the fixed points on the boundary and interior of a planar region

Electronic Journal of Qualitative Theory of Differential Equations
This paper tightens the classical Poincaré–Bendixson theory for a positively invariant, simply-connected compact set $\mathcal M$ in a continuously differentiable planar vector field by further characterizing for any point $p\in \mathcal M$, the ...
Pouria Ramazi, Ming Cao, Jacquelien Scherpen   +2 more
doaj   +1 more source

Modeling, dynamical analysis and numerical simulation of a new 3D cubic Lorenz-like system. [PDF]

Sci Rep, 2023
Wang H, Ke G, Pan J, Su Q.
europepmc   +1 more source

Some remarks on the Melnikov function

Electronic Journal of Differential Equations, 2002
We study the Melnikov function associated with a periodic perturbation of a differential equation having a homoclinic orbit. Our main interest is the characterization of perturbations that give rise to vanishing or non-vanishing of the Melnikov function.
Flaviano Battelli, Michal Feckan
doaj  

Nonlinear mechanism for the enhanced bursting activities induced by fast inhibitory autapse and reduced activities by fast excitatory autapse. [PDF]

Cogn Neurodyn, 2023
Qi C, Li Y, Gu H, Yang Y.
europepmc   +1 more source

Correction: An SIRS model with nonmonotone incidence and saturated treatment in a changing environment. [PDF]

J Math Biol, 2023
Pan Q, Huang J, Wang H.
europepmc   +1 more source