The residence time around different parts of a chaotic attractor is studied experimentally for nonlinear dynamical system with a double-scroll. It is shown that the dynamics of jumping from one scroll of the attractor to the other produces a distinct low-frequency peak in the otherwise...

We discuss the relation between ensemble and time averages for quasistationary states of low-dimensional symplectic maps that present remarkable analogies with similar states detected in many-body long-range-interacting Hamiltonian systems.

A macroscopic transport equation has been derived from the underlying microscopic dynamics and a general fluctuation-dissipation relation is proposed for a microscopic system composed of the collective degrees of freedom coupled to finite intrinsic ones through a weak interaction. With the aid...

Time complexity is associated with sensitive dependence on initial conditions and severe intrinsic predictability limits, in particular, the ‘butterfly effect’ paradigm: an exponential error growth and a corresponding characteristic predictability time. This was believed to be the universal...

We describe a novel mechanism for inducing traveling-wave attractors in rings of coupled maps. Traveling waves are easily produced when parameters controlling local dynamics vary from site to site. We also present some statistical results regarding the distribution of periodic time-evolutions.

In this paper, we construct low-dimensional manifolds of reduced description for equations of chemical kinetics from the standpoint of the method of invariant manifold (MIM). MIM is based on a formulation of the condition of invariance as an equation, and its solution by Newton iterations. A...

The propagation of virus infection fronts has been typically modeled using a set of classical (noncohabitation) reaction–diffusion equations for interacting species. However, for some single-species systems it has been recently shown that noncohabitation reaction–diffusion equations may lead...

The dynamics of dissipative and coherent N-body systems, such as a Bose–Einstein condensate, which can be described by an extended Gross–Pitaevskii formalism, is investigated. In order to analyze chaotic and unstable regimes, two approaches are considered: a metric one, based on calculations...

We review recent results obtained for the dynamics of incipient chaos. These results suggest a common picture underlying the three universal routes to chaos displayed by the prototypical logistic and circle maps. Namely, the period doubling, intermittency, and quasiperiodicity routes. In these...

Orthodox economic theory (utility maximization, rational agents, efficient markets in equilibrium) is based on arbitrarily postulated, nonempiric notions. The disagreement between economic reality and a key feature of neo-classical economic theory was criticized empirically by Osborne. I show...