Related papers: A New Hyperchaotic Attractor with Complex Patterns
The article discusses building models based on the reconstructed attractors of the time series. Discusses the use of the properties of dynamical chaos, namely to identify the strange attractors structure models. Here is used the group…
We study an infinite dimensional dynamical system that was proposed by J.C. Yoccoz and N.G. Yoccoz for modeling the population dynamics of some small rodents. We show an attractor exist in a large domain of the parameter space. Thanks to…
This paper is devoted to the study of nonautonomous multivalued semiflows and their associated pullback attractors. For this kind of dynamical systems we are able to characterize the upper and lower bounds of the attractor as complete…
In the first half of the paper, some recent advances in coupled dynamical systems, in particular, a globally coupled map are surveyed. First, dominance of Milnor attractors in partially ordered phase is demonstrated. Second, chaotic…
Study of continuous dynamical system through Poincare map is one of the most popular topics in nonlinear analysis. This is done by taking intersections of the orbit of flow by a hyper-plane parallel to one of the coordinate hyper-planes of…
Using examples we test formulae previously conjectured to give the fractal information dimension of chaotic repellors and their stable and unstable manifolds in ``typical'' dynamical systems in terms of the Lyapunov exponents and the…
We study nonlinear dynamics of two coupled contrast agents that are micro-meter size gas bubbles encapsulated into a viscoelastic shell. Such bubbles are used for enhancing ultrasound visualization of blood flow and have other promising…
Properties of the phase space of the standard map with memory are investigated. This map was obtained from a kicked fractional differential equation. Depending on the value of the parameter of the map and the fractional order of the…
The multiple time scale dynamics induced by radiation pressure and photothermal effects in a high-finesse optomechanical resonator is experimentally studied. At difference with two-dimensional slow-fast systems, the transition from the…
In the context of chaotic dynamical systems with exponential divergence of nearby trajectories in phase space, hyperchaos is defined as a state where there is divergence or stretching in at least two directions during the evolution of the…
This paper reveals some new and rich dynamics of a two-dimensional prey-predator system and to anticontrol the extinction of one of the species. For a particular value of the bifurcation parameter, one of the system variable dynamics is…
The long-term behaviour of solutions to a model for acoustic-structure interactions is addressed; the system is comprised of coupled semilinear wave (3D) and plate equations with nonlinear damping and critical sources. The questions of…
The asymmetrically forced, damped Duffing oscillator is introduced as a prototype model for analyzing the homoclinic tangle of symmetric dissipative systems with \textit{symmetry breaking} disturbances. Even a slight fixed asymmetry in the…
Many natural systems show emergent phenomena at different scales, leading to scaling regimes with signatures of chaos at large scales and an apparently random behavior at small scales. These features are usually investigated quantitatively…
We introduce a novel type of abnormal agents that proceed in the opposite direction of that defined for the normal agents. A new order parameter, $y$, is introduced to describe the characteristic of the system. Many interesting phenomenons…
A chaotic network of size $N$ with delayed interactions which resembles a pseudo-inverse associative memory neural network is investigated. For a load $\alpha=P/N<1$, where $P$ stands for the number of stored patterns, the chaotic network…
We analyze a multiparameter periodically-forced dynamical system inspired in the SIR endemic model. We show that the condition on the \emph{basic reproduction number} $\mathcal{R}_0 < 1$ is not sufficient to guarantee the elimination of…
We present a case study elaborating on the multiplicity and self-similarity of homoclinic and heteroclinic bifurcation structures in the 2D and 3D parameter spaces of a nonlinear laser model with a Lorenz-like chaotic attractor. In a…
A template describes the topological properties of a chaotic attractor. For attractors bounded by genus-1 torus, a linking matrix describes the topology of the template. It has been shown that the template depends on the Poincar\'e section…
For systems with hidden attractors and unstable equilibria, the property that hidden attractors are not connected with unstable equilibria is now accepted as one of their main characteristics. To the best of our knowledge this property has…