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Complexity, Volume 2024, Issue 1, 2024.We study the existence of fixed points, local stability analysis, bifurcation sets at fixed points, codimension‐one and codimension‐two bifurcation analysis, and chaos control in a predator‐prey model with Holling types I and III functional responses. It is proven that the model has a trivial equilibrium point for all involved parameters but interior ...
Abdul Qadeer Khan +4 more
wiley +1 more source
Dynamics of a New Four-Thirds-Degree Sub-Quadratic Lorenz-like System
AxiomsAiming to explore the subtle connection between the number of nonlinear terms in Lorenz-like systems and hidden attractors, this paper introduces a new simple sub-quadratic four-thirds-degree Lorenz-like system, where x˙=a(y−x), y˙=cx−x3z, z˙=−bz+x3y ...
Guiyao Ke +3 more
doaj +1 more source
Intersections of Lagrangian submanifolds and the Mel'nikov 1-form
, 2006 We make explicit the geometric content of Mel'nikov's method for detecting heteroclinic points between transversally hyperbolic periodic orbits.
Abraham +14 more
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Heteroclinic orbits for discrete Hamiltonian systems
, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiao, Huafeng, Long, Yuhua, Shi, Haiping
openaire +2 more sources
Construction of entire solutions for semilinear parabolic equations
Electronic Journal of Differential Equations, 2008 Entire solutions of parabolic equations (those which are defined for all time) are typically rather rare. For example, the heat equation has exactly one entire solution - the trivial solution.
Michael Robinson
doaj
Global portraits of inflation in nonsingular variables
European Physical Journal C: Particles and FieldsIn the phase space perspective, scalar field slow roll inflation is described by a heteroclinic orbit from a saddle type fixed point to a final attractive point.
Laur Järv, Dmitri Kraiko
doaj +1 more source
Prescribed energy connecting orbits for gradient systems
, 2019 We are concerned with conservative systems $\ddot{q}=\nabla V(q), \; q\in\mathbb{R}^N$ for a general class of potentials $V\in C^1(\mathbb{R}^N)$.
Alessio, Francesca +2 more
core +1 more source
Exponential dichotomies, heteroclinic orbits, and Melnikov functions
Journal of Differential Equations, 1990 The authors consider an n-dimensional perturbed system (*) \(dz/dt=g(z)+h(t,z,\epsilon),\) where the perturbation term h(t,z,\(\epsilon\)) is bounded, \(\epsilon\) being a multidimensional parameter, and they give, using the method of Lyapunov-Schmidt, a sufficient condition for the existence of a bounded solution of (*) as the solvability condition of
Battelli, Flaviano, Lazzari, Claudio
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Homoclinic orbits and chaos in a pair of parametrically-driven coupled nonlinear resonators
, 2010 We study the dynamics of a pair of parametrically-driven coupled nonlinear mechanical resonators of the kind that is typically encountered in applications involving microelectromechanical and nanoelectromechanical systems (MEMS & NEMS). We take advantage
A. Cleland +7 more
core +1 more source