Related papers: Complexity Analysis in Bouncing Ball Dynamical Sys…
The problem of error growth due to the incomplete knowledge of the evolution law which rules the dynamics of a given physical system is addressed. Major interest is devoted to the analysis of error amplification in systems with many…
We analyse how drag forces modify the orbits of objects moving through extended gaseous distributions. We consider how hydrodynamic (surface area) drag forces and dynamical friction (gravitational) drag forces drive the evolution of orbital…
We present an experimental study of the movement of individual particles in a layer of vertically shaken granular material. High-speed imaging allows us to investigate the motion of beads within one vibration period. This motion consists…
Given a dynamical system, we study the so-called space of shift functions thus introducing another vision on bifurcations and chaos. As an application of the obtained results, we give a partial solution to an open problem formulated in…
We study the dynamical interactions of mass systems in equilibrium under their own gravity that mutually exert and experience gravitational forces. The method we employ is to model the dynamical evolution of two isolated bars, hosted within…
Some dynamical properties of a bouncing ball model under the presence of an external force modeled by two nonlinear terms are studied. The description of the model is made by use of a two dimensional nonlinear measure preserving map on the…
Bifurcation analysis collects techniques for characterizing the dependence of certain classes of solutions of a dynamical system on variations in problem parameters. Common solution classes of interest include equilibria and periodic…
This paper attempts to make feasible the evolutionary emergence of novelty in a supposedly deterministic world which behavior is associated with those of the mathematical dynamical systems. The work was motivated by the observation of…
The dynamical symmetry breaking in a two-field model is studied by numerically solving the coupled effective field equations. These are dissipative equations of motion that can exhibit strong chaotic dynamics. By choosing very general model…
In a set of experiments, Couder et. al. demonstrate that an oscillating fluid bed may propagate a bouncing droplet through the guidance of the surface waves. We present a dynamical systems model, in the form of an iterative map, for a…
The theoretical and numerical understanding of the key concept of topological entropy is an important problem in dynamical systems. Most studies have been carried out on maps (discrete-time systems). We analyse a scenario of global changes…
Control of a hybrid dynamical system can manifest in one of two main ways: either through the continuous or the discrete dynamics. An example of controls influencing the continuous dynamics is legged locomotion, where the joints are…
Spatial diffusion of particles in periodic potential models has provided a good framework for studying the role of chaos in global properties of classical systems. Here a bidimensional "soft" billiard, classically modeled from an optical…
Based on the spectral decomposition technique, we introduce a simple and universal numerical method to analyze the stability of solitons. Adopting this method, the linear dynamical properties of $Q$-balls are systematically revealed, from…
We study fully three-dimensional droplets that slide down an incline by employing a thin-film equation that accounts for capillarity, wettability, and a lateral driving force in small-gradient (or long-wave) approximation. In particular, we…
A detailed set of experiments are described that capture over a 1000 different instances of the bounce of a golf ball. Video analysis is used to capture velocity and spin immediately prior to and subsequent to each bounce for a wide variety…
Strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of Lyapunov exponents. This regime,…
We study analytically the dynamics of a ball bouncing inelastically on a randomly vibrating platform, as a simple toy model of inelastic collapse. Of principal interest are the distributions of the number of flights n_f till the collapse…
We examine the dynamics of a particle in a general rotating quadratic potential, not necessarily stable or isotropic, using a general complex mode formalism. The problem is equivalent to that of a charged particle in a quadratic potential…
Motivated by the evolution of complex bird songs, an abstract imitation game is proposed to study the increase of dynamical complexity: Artificial "birds" display a "song" time series to each other, and those that imitate the other's song…