Related papers: Nonintegrability, Chaos, and Complexity
Chaotic dynamical systems with two or more attractors lying on invariant subspaces may, provided certain mathematical conditions are fulfilled, exhibit intermingled basins of attraction: Each basin is riddled with holes belonging to basins…
Devising optimal interventions for constraining stochastic systems is a challenging endeavour that has to confront the interplay between randomness and nonlinearity. Existing methods for identifying the necessary dynamical adjustments…
It is demonstrated that power-laws which are modified by logarithmic corrections arise in supercorrelated systems. Their characteristic feature is the energy attributed to a state (or value of a general cost function) which depends…
We analyze a diffuse interface model for multi-phase flows of $N$ incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smooth domain existence of weak solutions in two and three space…
We show that dense active fluids comprising interacting particles with persistent self-propulsion are driven to a non-equilibrium steady state consisting of co-moving particles with co-aligned active forces. This velocity and force sorting…
Nonconservative evolution problems describe irreversible processes and dissipative effects in a broad variety of phenomena. Such problems are often characterised by a conservative part, which can be modelled as a Hamiltonian term, and a…
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…
For general dissipative dynamical systems we study what fraction of solutions exhibit chaotic behavior depending on the dimensionality $d$ of the phase space. We find that a system of $d$ globally coupled ODE's with quadratic and cubic…
Dissipative phenomena manifest in multiple mechanical systems. In this dissertation, different geometric frameworks for modelling non-conservative dynamics are considered. The objective is to generalize several results from conservative…
The paper considers some class of dynamical systems that called density systems. For such systems the derivative of quadratic function depends on so-called density function. The density function is used to set the properties of phase space,…
We study the long-time behavior of global strong solutions to a hydrodynamic system for nonhomogeneous incompressible nematic liquid crystal flows driven by two types of external forces in a smooth bounded domain in $\mathbb{R}^2$. For…
Driven-dissipative systems define a broad class of non-equilibrium systems where an external drive (e.g. laser) competes with a dissipative environment. The steady state of dynamics is generically distinct from a thermal state…
We show that a noncommutative dynamical system of the type that occurs in quantum theory can often be associated with a dynamical principle; that is, an infinitesimal structure that completely determines the dynamics. The nature of these…
Non-reciprocal systems have been shown to sustain time-dependent patterns, most prominently travelling waves. The transition into these time-dependent states generally breaks time-translational invariance, representing a clear deviation…
To date it has not been possible to prove whether or not the three-dimensional incompressible Euler equations develop singular behaviour in finite time. Some possible singular scenarios, as for instance shock-waves, are very important from…
Following an approach of the second author for conformally invariant variational problems in two dimensions, we show in four dimensions the existence of a conservation law for fourth order systems, which includes both intrinsic and…
Dissipation using a finite environment coupled to a single harmonic oscillator have been studied quite extensively. We extend the study by looking at the dynamics of the dissipation when we introduce a second bath of N identical quartic…
Regarding Ricci flow as a dynamical system, we derive sufficient conditions for noncompact stationary (Ricci-flat) solutions to possess infinite-dimensional unstable manifolds, and provide examples satisfying those criteria that have…
We consider the critical dynamics of a system with an $n$-component non-conserved order parameter coupled to a conserved field with long range diffusion. An exponent $\sigma$ characterizes the long range transport, $\sigma=2$ being the…
We consider space-time correlations in driven diffusive systems which undergo a fluctuation into a regime with an atypically large current or dynamical activity. For a single conserved mass we show that the spatio-temporal density…