Related papers: A model for dynamical systems with strange attract…
The complication of chaotic oscillation under its transformation by linear inertial process is discussed. It is shown that such complication is begun from large scales of attractor and is pure dynamical process.
Attractors of cooperative dynamical systems are particularly simple; for example, a nontrivial periodic orbit cannot be an attractor. This paper provides characterizations of attractors for the wider class of coherent systems, defined by…
An attractor of a piecewise-smooth continuous system of differential equations can bifurcate from a stable equilibrium to a more complicated invariant set when it collides with a switching manifold under parameter variation. Here numerical…
We investigate an oscillator linearly coupled with a one-dimensional Ising system. The coupling gives rise to drastic changes both in the oscillator statics and dynamics. Firstly, there appears a second order phase transition, with the…
The R\"ossler system is one of the best known chaotic dynamical systems, generating a chaotic attractor which, by the numerical evidence, arises by a period-doubling route to chaos. In this paper we state and prove a topological criterion…
We use the integrable deformations method for a three-dimensional system of differential equations to obtain deformations of the T system. We analyze a deformation given by particular deformation functions. We point out that the obtained…
We investigate the dynamical coupling between the motion and the deformation of a single self-propelled domain based on two different model systems in two dimensions. One is represented by the set of ordinary differential equations for the…
The problem of damping a system of linear oscillators is considered. The problem is solved by using a control in the form of dry friction. The motion of the system under the control is governed by a system of differential equations with…
Forced oscillation of a system composed of two pendulums coupled by a spring in the presence of damping is investigated. In the steady state and within the small angle approximation we solve the system equations of motion and obtain the…
A certain class of integrable hydrodynamic type systems with three independent and N dependent variables is considered. We choose the existence of a pseudopotential as a criterion of integrability. It turns out that the class of integrable…
In this paper, based on the classic Chua's circuit, a charge-controlled memristor is introduced to design a novel four-dimensional chaotic system. The complex dynamics of the novel chaotic system such as equilibrium points, stability,…
We demonstrate experimental exploration of the attractor diagram of an optomechanical system where the optical forces compensate for the mechanical losses. In this case stable self-induced oscillations occur but only for specific mirror…
Dynamical equations are formulated and a numerical study is provided for self-oscillatory model systems based on the triple linkage hinge mechanism of Thurston -- Weeks -- Hunt -- MacKay. We consider systems with holonomic mechanical…
We investigate the dynamics of a three-dimensional system modeling a molecular mechanism for the circadian rhythm in Drosophila. We first prove the existence of a compact attractor in the region with biological meaning. Under the assumption…
In this paper, I aim to study free oscillations of a system of oscillators in more than one dimensions in the absence of damping. The basic approach lies in decoupling the motion in the individual perpendicular directions. Once the…
Examples of one-dimensional lattice systems are considered, in which patterns of different spatial scales arise alternately, so that the spatial phase over a full cycle undergo transformation according to expanding circle map that implies…
We employ variational Monte Carlo methods to study the transition to strange matter in a simple one-dimensional string-flip model with two flavors and two colors of quarks. The dynamics of the system are described in terms of a many-body…
A chaotic system under periodic forcing can develop a periodically visited strange attractor. We discuss simple models in which the phenomenon, quite easy to see in numerical simulations, can be completely studied analytically.
Properties of an infinite system of nonlinearly coupled ordinary differential equations are discussed. This system models some properties present in the equations of motion for an inviscid fluid such as the skew symmetry and the…
The wave equation with energy critical sources and nonlinear damping defined on a 3D bounded domain is considered. It is shown that the resulting dynamical system admits a global attractor. Under the additional assumption of strong…