Displaying similar documents to “A convergence criterion for monotone global dynamical systems.”

Periodic parametric perturbation control for a 3D autonomous chaotic system and its dynamics at infinity

Zhen Wang, Wei Sun, Zhouchao Wei, Shanwen Zhang (2017)

Kybernetika

Similarity:

Periodic parametric perturbation control and dynamics at infinity for a 3D autonomous quadratic chaotic system are studied in this paper. Using the Melnikov's method, the existence of homoclinic orbits, oscillating periodic orbits and rotating periodic orbits are discussed after transferring the 3D autonomous chaotic system to a slowly varying oscillator. Moreover, the parameter bifurcation conditions of these orbits are obtained. In order to study the global structure, the dynamics...

On the preservation of combinatorial types for maps on trees

Lluís Alsedà, David Juher, Pere Mumbrú (2005)

Annales de l'institut Fourier

Similarity:

We study the preservation of the periodic orbits of an A -monotone tree map f : T ⟶ T in the class of all tree maps g : S ⟶ S having a cycle with the same pattern as A . We prove that there is a period-preserving injective map from the set of (almost all) periodic orbits of f into the set of periodic orbits of each map in the class. Moreover, the relative positions of the corresponding orbits in the trees T and S (which need not be homeomorphic) are essentially preserved.

Smoothness of the attractor of almost all solutions of a delay differential equation

Walther Hans-Otto, Yebdri Mustapha

Similarity:

AbstractLet a C¹-function f:ℝ → ℝ be given which satisfies f(0) = 0, f'(ξ) < 0 for all ξ ∈ ℝ, and sup f < ∞ or -∞ < inf f. Let C = C([-1,0],ℝ). For an open-dense set of initial data the phase curves [0,∞) → C given by the solutions [-1,∞) → ℝ to the negative feedback equationx'(t) = -μx(t) + f(x(t-1)), with μ > 0,are absorbed into the positively invariant set S ⊂ C of data ϕ ≠ 0 with at most one sign change. The global attractor A of the semiflow restricted to S̅ is either...