Related papers: Complexity Analysis in Bouncing Ball Dynamical Sys…
Most complex systems are intrinsically dynamic in nature. The evolution of a dynamic complex system is typically represented as a sequence of snapshots, where each snapshot describes the configuration of the system at a particular instant…
We consider two minimal models of active fluid droplets that exhibit complex dynamics including steady motion, deformation, rotation and oscillating motion. First we consider a droplet with a concentration of active contractile matter…
This paper is concerned with the problem of an ellipsoid of revolution rolling on a horizontal plane under the assumption that there is no slipping at the point of contact and no spinning about the vertical. A reduction of the equations of…
Some dynamical properties of non interacting particles in a bouncer model are described. They move under gravity experiencing collisions with a moving platform. The evolution to steady state is described in two cases for dissipative…
Chaotic properties of symmetrical two-dimensional stadium-like billiards with elliptical arcs are studied numerically and analytically. For the two-parameter truncated elliptical billiard the existence and linear stability of several…
This paper investigates the dynamics and integrability of the double spring pendulum, which has great importance in studying nonlinear dynamics, chaos, and bifurcations. Being a Hamiltonian system with three degrees of freedom, its analysis…
Time-dependent potentials are common in galactic systems that undergo significant evolution, interactions, or encounters with other galaxies, or when there are dynamic processes like star formation and merging events. Recent studies show…
Dynamics of inelastic gases are studied within the framework of random collision processes. The corresponding Boltzmann equation with uniform collision rates is solved analytically for gases, impurities, and mixtures. Generally, the energy…
We present a numerical investigation of the dynamics of one falling oblate ellipsoid particle in a viscous fluid, in three dimensions, using a constrained-force technique \cite{Kai}, \cite{Kaih} and \cite{Esa}. We study the dynamical…
The motion of a particle that suffers the influence of simple inner (outer) periodic perturbations when it evolves around a center of attraction modeled by an inverse square law plus a quadrupole-like term is studied. The equations of…
We study the classical and quantum mechanics of a three-dimensional stadium billiard. It consists of two quarter cylinders that are rotated with respect to each other by 90 degrees, and it is classically chaotic. The billiard exhibits only…
We here describe the possibility of a synthetic description of the onset of Chaos in many degrees of freedom dynamical systems within the framework of the geometric description of dynamics. We show how this approach to instability helps to…
In Physics, we have laws that determine the time evolution of a given physical system, depending on its parameters and its initial conditions. When we have multi-stable systems, many attractors coexist so that their basins of attraction…
We study a generalized three-dimensional stadium billiard and present strong numerical evidence that this system is completely chaotic. In this convex billiard chaos is generated by the defocusing mechanism. The construction of this…
We study the evolution of cosmological perturbations in a non-singular bouncing cosmology with a bounce phase which has superimposed oscillations of the scale factor. We identify length scales for which the final spectrum of fluctuations…
The emergence of cosmic structure is commonly considered one of the most complex phenomena in Nature. However, this complexity has never been defined nor measured in a quantitative and objective way. In this work we propose a method to…
Bifurcation theory is the usual analytic approach to study the parameter space of a dynamical system. Despite the great power of prediction of these techniques, fundamental limitations appear during the study of a given problem. Nonlinear…
Over the past decade the study of fluidic droplets bouncing and skipping (or ``walking'') on a vibrating fluid bath has gone from an interesting experiment to a vibrant research field. The field exhibits challenging fluids problems,…
The evolution of self-gravitating systems, and long-range interacting systems more generally, from initial configurations far from dynamical equilibrium is often described as a simple two phase process: a first phase of violent relaxation…
In the present work we have developed a three-dimensional gravitational model of barred galaxies, in order to study orbital and escape dynamics of the stars inside their central barred region. Our gravitational model is composed of four…