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We study the dynamics of a "kicked" quantum system undergoing repeated measurements of momentum. A diffusive behavior is obtained for a large class of Hamiltonians, even when the dynamics of the classical counterpart is not chaotic. These…
The emergence of nontrivial collective behavior in networks of coupled chaotic maps is investigated by means of a nonlinear mutual prediction method. The resulting prediction error is used to measure the amount of information that a local…
The abundance of data affords researchers to pursue more powerful computational tools to learn the dynamics of complex system, such as neural networks, engineered systems and social networks. Traditional machine learning approaches capture…
Hamiltonian learning protocols are essential tools to benchmark quantum computers and simulators. Yet rigorous methods for time-dependent Hamiltonians and Lindbladians remain scarce despite their wide use. We close this gap by learning the…
Nonlinear and non-stationary processes are prevalent in various natural and physical phenomena, where system dynamics can change qualitatively due to bifurcation phenomena. Traditional machine learning methods have advanced our ability to…
An extremely challenging problem of significant interest is to predict catastrophes in advance of their occurrences. We present a general approach to predicting catastrophes in nonlinear dynamical systems under the assumption that the…
Contraction theory is a recently developed dynamic analysis and nonlinear control system design tool based on an exact differential analysis of convergence. This paper extends contraction theory to local and global stability analysis of…
Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…
Two different aspects of formation control of multiple agents subjected to linear transformation have been addressed in this paper. We consider a set of complex single integrator systems so that the dimension of the system reduces to half…
A method to estimate Lyapunov spectra from spatio-temporal data is presented, which is well-suited to be applied to experimental situations. It allows to characterize the high-dimensional chaotic states, with possibly a large number of…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
In this paper we introduce an iterative Jacobi algorithm for solving distributed model predictive control (DMPC) problems, with linear coupled dynamics and convex coupled constraints. The algorithm guarantees stability and persistent…
We consider two related tasks: (a) estimating a parameterisation of a given Gibbs state and expectation values of Lipschitz observables on this state; and (b) learning the expectation values of local observables within a thermal or quantum…
Small-sized systems exhibit a finite number of routes to chaos. However, in extended systems, not all routes to complex spatiotemporal behavior have been fully explored. Starting from the sine-Gordon model of parametrically driven chain of…
We examine characteristic properties of deterministic and stochastic diffusion in low-dimensional chaotic dynamical systems. As an example, we consider a periodic array of scatterers defined by a simple chaotic map on the line. Adding…
We present a numerical method for learning unknown nonautonomous stochastic dynamical system, i.e., stochastic system subject to time dependent excitation or control signals. Our basic assumption is that the governing equations for the…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…
Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…
Motivated by applications in optics and acoustics we develop a dynamical-system approach to describe absorption in chaotic systems. We introduce an operator formalism from which we obtain (i) a general formula for the escape rate $\kappa$…
A novel method for stability and instability study of autonomous dynamical systems using the flow and divergence of the vector field is proposed. A relation between the method of Lyapunov functions and the proposed method is established.…