Embedding inverse limits interval maps as attractors
Epidemiology of Dengue Fever: A Model with Temporary Cross-Immunity and Possible Secondary Infection Shows Bifurcations and Chaotic Behaviour in Wide Parameter Regions
Basic models suitable to explain the epidemiology of dengue fever have previously shown the possibility of deterministically chaotic attractors, which might explain the observed fluctuations found in empiric outbreak data. However, the region of bifurcations and chaos require strong enhanced infectivity on secondary infection, motivated by experimental findings of antibody-dependent-enhancement. Including temporary cross-immunity in such models, which is common knowledge among field researchers...
Equivalence between subshrubs and chaotic bands in the Mandelbrot set.
Ergodic theory approach to chaos: Remarks and computational aspects
We discuss basic notions of the ergodic theory approach to chaos. Based on simple examples we show some characteristic features of ergodic and mixing behaviour. Then we investigate an infinite dimensional model (delay differential equation) of erythropoiesis (red blood cell production process) formulated by Lasota. We show its computational analysis on the previously presented theory and examples. Our calculations suggest that the infinite dimensional model considered possesses an attractor of a...
Essential dynamics for Lorenz maps on the real line and the lexicographical world
Eventually periodic points of infra-nil endomorphisms.
Examples of minimal diffeomorphisms on 𝕋² semiconjugate to an ergodic translation
We prove that for every ϵ > 0 there exists a minimal diffeomorphism f: ² → ² of class and semiconjugate to an ergodic translation with the following properties: zero entropy, sensitivity to initial conditions, and Li-Yorke chaos. These examples are obtained through the holonomy of the unstable foliation of Mañé’s example of a derived-from-Anosov diffeomorphism on ³.
Existence of pullback attractors for the coupled suspension bridge equations.
Existence of unique SRB-measures is typical for real unicritical polynomial families
Flow around a slender circular cylinder: a case study on distributed Hopf bifurcation.
Fractal Newton basins.
Fractalidad extrema e indeterminación clásica en sistemas dinámicos.
From the theorem of Ważewski to computer assisted proofs in dynamics
Generalized Hénon difference equations with delay.
Generate -scroll attractor via composite switching controls.
Generic chaos
Global dynamics of a competitive system of rational difference equations in the plane.
Global synchronization of chaotic Lur’e systems via replacing variables control
Finding sufficient criteria for synchronization of master-slave chaotic systems by replacing variables control has been an open problem in the field of chaos control. This paper presents some recent works on the subject, with emphasis on chaos synchronization of both identical and parametrically mismatched Lur’e systems by replacing variables control. The synchronization schemes are formally constructed and two classes of sufficient criteria for global synchronization, linear matrix inequality criterion...
Higher dimensional Melnikov mappings
Hopf bifurcation analysis of some hyperchaotic systems with time-delay controllers
A four-dimensional hyperchaotic Lü system with multiple time-delay controllers is considered in this paper. Based on the theory of Hopf bifurcation in delay system, we obtain a simple relationship between the parameters when the system has a periodic solution. Numerical simulations show that the assumption is a rational condition, choosing parameter in the determined region can control hyperchaotic Lü system well, the chaotic state is transformed to the periodic orbit. Finally, we consider the differences...