Related papers: Non-deterministic dynamics of a mechanical system
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…
Many different definitions of computational universality for various types of dynamical systems have flourished since Turing's work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical…
An exact transformation method is introduced that reduces the governing equations of a continuum structure coupled to strong nonlinearities to a low dimensional equation with memory. The method is general and well suited to problems with…
A method to quantify robust performance for situations where structured parameter variations and initial state errors rather than extraneous disturbances are the main performance limiting factors is presented. The approach is based on the…
Determining the reachable set for a given nonlinear control system is crucial for system control and planning. However, computing such a set is impossible if the system's dynamics are not fully known. This paper is motivated by a scenario…
The necessity and benefit of singular solutions in the study of physical systems is shown. By singular solutions we mean solutions that are not contained in the general solution of the system of equations that describes the dynamic system…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. In this way, a physical clock with discrete…
We study three different experiments that involve dry friction and periodic driving, and which employ both single and many-particle systems. These experimental set-ups, besides providing a playground for investigation of frictional effects,…
The dynamical properties of a particle in a gravitational field colliding with a rigid wall moving with piecewise constant velocity are studied. The linear nature of the wall's motion permits further analytical investigation than is…
It is ``folklore'' that the solution to a set reachability problem for a dynamical system is only noncomputable because of non-robustness reasons. A robustness condition that can be imposed on a dynamical system is the requirement of the…
We present a theory for Coulomb drag between two mesoscopic systems. Our formalism expresses the drag in terms of scattering matrices and wave functions, and its range of validity covers both ballistic and disordered systems. The…
The well-defined but intricate course of time evolution exhibited by many naturally occurring phenomena suggests some source of dynamic order sustaining it. In spite of its obviousness as a problem, it has remained absent from the…
Chronotaxic systems represent deterministic nonautonomous oscillatory systems which are capable of resisting continuous external perturbations while having a complex time-dependent dynamics. Until their recent introduction in \emph{Phys.…
We study local features, and provide a topological insight into the global structure of the probability density distribution and of the pattern of the optimal paths for large rare fluctuations away from a stable state. In contrast to…
We consider quantum Hamiltonian systems composed of mutually interacting "dynamical subsystem" with one or several degrees of freedom and "thermostat" with arbitrary many degrees of freedom, under assumptions that the interaction ensures…
Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the…
In light of G\"{o}del's undecidability results (incomplete theorems) for math, quantum indeterminism indicates that physics and the Universe may be indeterministic, incomplete, and open in nature, and therefore demand no single unification…
Dynamics of systems of structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. The…
The dynamics of a non-autonomous oscillator in which the phase and frequency of the external force depend on the dynamical variable is studied. Such a control of the phase and frequency of the external force leads to the appearance of…
When complex systems are driven to extinction by some external factor, their non-stationary dynamics can present an intermittent behaviour between relative tranquility and burst of activity whose consequences are often catastrophic. To…