Related papers: Sensitivity of Wave Field Evolution and Manifold S…
We investigate the sensitivity of quantum systems that are chaotic in a classical limit, to small perturbations of their equations of motion. This sensitivity, originally studied in the context of defining quantum chaos, is relevant to…
The evolution of a passive scalar field is considered for a slowly varying stratified medium, which is convected in an incompressible sheared flow with many overlapping static flux islands. Within the quasilinear/random phase approximation,…
The properties of long, numerically-determined periodic orbits of two low-dimensional chaotic systems, the Lorenz equations and the Kuramoto-Sivashinsky system in a minimal-domain configuration, are examined. The primary question is to…
Robustness to mutations and noise has been shown to evolve through stabilizing selection for optimal phenotypes in model gene regulatory networks. The ability to evolve robust mutants is known to depend on the network architecture. How do…
What features characterise complex system dynamics? Power laws and scale invariance of fluctuations are often taken as the hallmarks of complexity, drawing on analogies with equilibrium critical phenomena[1-3]. Here we argue that slow,…
A strong analogy is found between the evolution of localized disturbances in extended chaotic systems and the propagation of fronts separating different phases. A condition for the evolution to be controlled by nonlinear mechanisms is…
This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…
Intrinsic instability of trajectories characterizes chaotic dynamical systems. We report here that trajectories can exhibit a surprisingly high degree of stability, over a very long time, in a chaotic dynamical system. We provide a detailed…
The dynamics of hexagon patterns in rotating systems are investigated within the framework of modified Swift-Hohenberg equations that can be considered as simple models for rotating convection with broken up-down symmetry, e.g.…
Diverse biological networks exhibit universal features distinguished from those of random networks, calling much attention to their origins and implications. Here we propose a minimal evolution model of Boolean regulatory networks, which…
Stable and unstable manifolds, originating from hyperbolic cycles, fundamentally characterize the behaviour of dynamical systems in chaotic regions. This letter demonstrates that their shifts under perturbation, crucial for chaos control,…
Recent experimental and theoretical studies on the magnetization dynamics driven by an electric current have uncovered a number of unprecedented rich dynamic phenomena. We predict an intrinsic chaotic dynamics that has not been previously…
Classical chaotic systems are distinguished by their sensitive dependence on initial conditions. The absence of this property in quantum systems has lead to a number of proposals for perturbation-based characterizations of quantum chaos,…
Defect-chaos is studied numerically in coupled Ginzburg-Landau equations for parametrically driven waves. The motion of the defects is traced in detail yielding their life-times, annihilation partners, and distances traveled. In a regime in…
In presence of unstable dimension variability numerical solutions of chaotic systems are valid only for short periods of observation. For this reason, analytical results for systems that exhibit this phenomenon are needed. Aiming to go one…
An area-preserving map of the unit sphere, consisting of alternating twists and turns, is mostly chaotic. A Liouville density on that sphere is specified by means of its expansion into spherical harmonics. That expansion initially…
Recently a Hamiltonian formulation for the evolution of the universe dominated by multiple oscillatory scalar fields was developed by the present author and was applied to the investigation of the evolution of cosmological perturbations on…
Two-dimensional decaying turbulent flow is known to approach apparently stable states after a long time evolution. A few theories and models have been so far proposed to account for this relaxation. In this paper, we compare results of…
A well-behaved adjoint sensitivity technique for chaotic dynamical systems is presented. The method arises from the specialisation of established variational techniques to the unstable periodic orbits of the system. On such trajectories,…
Recent work on gravitational geons is extended to examine the stability properties of gravitational and electromagnetic geon constructs. All types of geons must possess the property of regularity, self-consistency and quasi-stability on a…