Related papers: Dimensional-invariance principles in coupled dynam…
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…
A dynamical systems approach to turbulence envisions the flow as a trajectory through a high-dimensional state space transiently visiting the neighbourhoods of unstable simple invariant solutions (E. Hopf, Commun. Appl. Maths 1, 303, 1948).…
This paper is concerned with the estimation of time-varying networks for high-dimensional nonstationary time series. Two types of dynamic behaviors are considered: structural breaks (i.e., abrupt change points) and smooth changes. To…
This work investigates the out-of-equilibrium dynamics of dipole and higher-moment conserving systems with long-range interactions, drawing inspiration from trapped ion experiments in strongly tilted potentials. We introduce a hierarchical…
The behaviour of many real-world phenomena can be modelled by nonlinear dynamical systems whereby a latent system state is observed through a filter. We are interested in interacting subsystems of this form, which we model by a set of…
Top-tier parallel computing clusters continue to accumulate more and more computational power with more and better CPUs and Networks. This allows, especially for environmental simulations, computations with larger domain sizes and better…
We study spatiotemporal intermittency in a system of coupled sine circle maps. The phase diagram of the system shows parameter regimes where the STI lies in the directed percolation class, as well as regimes which show pure spatial…
Many recent machine learning models rely on fine-grained dynamic control flow for training and inference. In particular, models based on recurrent neural networks and on reinforcement learning depend on recurrence relations, data-dependent…
One of the outstanding problems in complexity science and dynamical system theory is understanding the dynamic behavior of high-dimensional networked systems and their susceptibility to transitions to undesired states. Because of varied…
We study the transport properties of passive inertial particles in a $2-d$ incompressible flows. Here the particle dynamics is represented by the $4-d$ dissipative embedding map of $2-d$ area-preserving standard map which models the…
A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…
Instabilities and pattern formation is the rule in nonequilibrium systems. Selection of a persistent lengthscale, or coarsening (increase of the lengthscale with time) are the two major alternatives. When and under which conditions one…
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…
This paper considers discontinuous dynamical systems, i.e., systems whose associated vector field is a discontinuous function of the state. Discontinuous dynamical systems arise in a large number of applications, including optimal control,…
We develop a general criterion about coarsening for a class of nonlinear evolution equations describing one dimensional pattern-forming systems. This criterion allows one to discriminate between the situation where a coarsening process…
In this paper, we study pinning control problem of coupled dynamical systems with stochastically switching couplings and stochastically selected controller-node set. Here, the coupling matrices and the controller-node sets change with time,…
This paper considers the problem of designing a continuous-time dynamical system that solves a constrained nonlinear optimization problem and makes the feasible set forward invariant and asymptotically stable. The invariance of the feasible…
Invariant manifolds are important sets arising in the stability theory of dynamical systems. In this article, we take a brief review of invariant sets. We provide some results regarding the existence of invariant lines and parabolas in…
We introduce a new set of flow parameters to describe the time dependence of the equation of state and the speed of sound in single field cosmological models. A scale invariant power spectrum is produced if these flow parameters satisfy…
This paper proposes two nonlinear dynamics to solve constrained distributed optimization problem for resource allocation over a multi-agent network. In this setup, coupling constraint refers to resource-demand balance which is preserved at…