Dynamical Critical Phenomena in Driven-Dissipative Systems

Complexity in Hamiltonian-driven dissipative chaotic dynamical systems.

The existence of symmetry in chaotic dynamical systems often leads to one or several low-dimensional invariant subspaces in the phase space. We demonstrate that complex behaviors can arise when the dynamics in the invariant subspace is Hamiltonian but the full system is dissipative. In particular, an infinite number of distinct attractors can coexist. These attractors can be quasiperiodic, stra...

High-Dimensional Chaos in dissipative and Driven Dynamical Systems

Studies of nonlinear dynamical systems with many degrees of freedom show that the behavior of these systems is significantly different as compared with the behavior of systems with less than two degrees of freedom. These findings motivated us to carry out a survey of research focusing on the behavior of high-dimensional chaos, which include onset of chaos, routes to chaos, and the persistence o...

Dissipative Dynamical Systems

On Differentially Dissipative Dynamical Systems

Dissipativity is an essential concept of systems theory. The paper provides an extension of dissipativity, named differential dissipativity, by lifting storage functions and supply rates to the tangent bundle. Differential dissipativity is connected to incremental stability in the same way as dissipativity is connected to stability. It leads to a natural formulation of differential passivity wh...

observational dynamical systems

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