Related papers: Fractal Evolution of Normalized Feedback Systems o…
Nonlinear dynamical systems, ranging from insect populations to lasers and chemical reactions, might exhibit sensitivity to small perturbations in their control parameters, resulting in uncertainties on the predictability of tunning…
Frequency domain analysis of linear time-invariant (LTI) systems in feedback with static nonlinearities is a classical and fruitful topic of nonlinear systems theory. We generalize this approach beyond equilibrium stability analysis with…
A time dependent variational approach is used to derive the equations of motion for the \lambda \phi^4 model. The simultaneous evolution of the quantum fluctuations and of the classical part of the field is considered in a lattice of 1+1…
Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets…
Self-consistent dynamical approximations for strongly correlated fermion systems are particularly successful in capturing the dynamical competition of local correlations. In these, the effect of spatially extended degrees of freedom is…
"\textit{The noise is the signal}"[R. Landauer, Nature \textbf{392}, 658 (1998)] emphasizes the rich information content encoded in fluctuations. This paper assesses the dynamical role of fluctuations of a quantum system driven far from…
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…
This paper presents a data-integrated framework for learning the dynamics of fractional-order nonlinear systems in both discrete-time and continuous-time settings. The proposed framework consists of two main steps. In the first step,…
We propose a lattice model for Dirac fermions which allows us to break the degeneracy of the node structure. In the presence of a random gap we analyze the scaling behavior of the localization length as a function of the system width within…
Modelling stochastic systems has many important applications. Normal form coordinate transforms are a powerful way to untangle interesting long term macroscale dynamics from detailed microscale dynamics. We explore such coordinate…
We study, using numerical simulations, the dynamical evolution of self-gravitating point particles in static euclidean space, starting from a simple class of infinite ``shuffled lattice'' initial conditions. These are obtained by applying…
We investigate the time dependent Ginzburg-Landau (TDGL) equation for a non conserved order parameter on an infinitely ramified (deterministic) fractal lattice employing two alternative methods: the auxiliary field approach and a numerical…
We consider transformations of deterministic and random signals governed by simple dynamical mappings. It is shown that the resulting signal can be a random process described in terms of fractal distributions and fractal domain integrals.…
In two recent articles a detailed study has been presented of the out of equilibrium dynamics of an infinite system of self-gravitating points initially located on a randomly perturbed lattice. In this article we extend the treatment of the…
We study collisions between nearly planar domain walls including the effects of small initial nonplanar fluctuations. These perturbations represent the small fluctuations that must exist in a quantum treatment of the problem. In a previous…
In quantum/wave systems with chaotic classical analogs, wavefunctions evolve in highly complex, yet deterministic ways. A slight perturbation of the system, though, will cause the evolution to diverge from its original behavior increasingly…
Stochastic feedback systems give rise to a variety of notions of stability. The conditions for the stability of the median, mean, and variance stability conditions differ. These conditions can be stated explicitly for scalar discrete-time…
This paper addresses the design of finite-dimensional feedback control laws for linear discrete-time fractional-order systems with additive state disturbance. A set of sufficient conditions are provided to guarantee convergence of the state…
Processes occurring in real open systems are far from equilibrium state and they can lead to synergetic effects, which are caused by coordinated behavior of system units. Traditional methods of analysis often just establish such behavior,…
We examine when differentially flat nonlinear control systems with more than two inputs can be rendered static feedback linearizable by a minimal number of prolongations of suitably chosen inputs after applying a static input…