Related papers: Dynamics under Geometric Dissipation
In order to study the behaviour of discrete dynamical systems under adiabatic cyclic variations of their parameters, we consider discrete versions of adiabatically-rotated rotators. Paralleling the studies in continuous systems, we…
The recently proposed definition of complexity for static and spherically symmetric self--gravitating systems [1], is extended to the fully dynamic situation. In this latter case we have to consider not only the complexity factor of the…
The stability criteria for spatially flat homogeneous and isotropic cosmological dynamical system is investigated with the interaction of a scalar field endowed with a perfect fluid.In this paper, we depict the dynamical system perspective…
We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is…
We here describe the possibility of a synthetic description of the onset of Chaos in many degrees of freedom dynamical systems within the framework of the geometric description of dynamics. We show how this approach to instability helps to…
A systematic asymptotic expansion is developed for the gravitational wave degrees of freedom of a class of expanding, vacuum Gowdy cosmological spacetimes. In the wave map description of these models, the evolution of the gravitational wave…
In this paper we consider the global stability of solutions of a nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable linear autonomous equation with unique zero equilibrium where…
In this communication, complex systems with a near trivial dynamics are addressed. First, under the hypothesis of equiprobability in the asymptotic equilibrium, it is shown that the (hyper) planar geometry of an $N$-dimensional multi-agent…
Physical experiments and numerical simulations have revealed a remarkable stabilizing phenomenon: a background magnetic field stabilizes and dampens electrically conducting fluids. This paper provides a rigorous mathematical justification…
We provide a constructive method designed in order to control the stability of a given periodic orbit of a general completely integrable system. The method consists of a specific type of perturbation, such that the resulting perturbed…
This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation subject to a nonmonotone distributed damping. A well-posedness result is provided together with a precise characterization of the asymptotic…
A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical…
Spatial structure can arise in spatial point process models via a range of mechanisms, including neighbour-dependent directionally biased movement. This spatial structure is neglected by mean-field models, but can have important effects on…
In this paper we apply the method of Lagrangian descriptors to explore the geometrical structures in phase space that govern the dynamics of dissipative systems. We demonstrate through many classical examples taken from the nonlinear…
Dynamical systems that describe the escape from the basins of attraction of stable invariant sets are presented and analyzed. It is shown that the stable fixed points of such dynamical systems are the index-1 saddle points. Generalizations…
In this work we study the asymptotic behavior of a class of damped second-order gradient systems $$ \ddot{u}(t) + a\dot{u}(t) + \nabla W(u(t)) = 0, $$ under assumptions ensuring local convexity of the potential near equilibrium and…
We present examples of exponential stabilization for the damped wave equation on a compact manifold in situations where the geometric control condition is not satisfied. This follows from a dynamical argument involving a topological…
The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…
In this paper we present a new approach for studying the dynamics of spatially inhomogeneous cosmological models with one spatial degree of freedom. By introducing suitable scale-invariant dependent variables we write the evolution…
In a composite system of gravitationally coupled stellar and gaseous discs, we perform linear stability analysis for axisymmetric coplanar perturbations using the two-fluid formalism. The background stellar and gaseous discs are taken to be…