Related papers: Nonlinear analog of the complexity-stability trans…
We consider systems characterized by the presence of a rapidly oscillating force. A general method is presented for the construction of the effective action governing the large-scale nonlinear dynamics of such systems order by order in…
We describe and demonstrate a method to reconstruct an amplitude equation from the nonlinear relaxation dynamics in the succession of the Rosensweig instability. A flat layer of a ferrofluid is cooled such that the liquid has a relatively…
We develop a numerical approach to reconstruct the phase dynamics of driven or coupled self-sustained oscillators. Employing a simple algorithm for computation of the phase of a perturbed system, we construct numerically the equation for…
One-dimensional run-and-tumble processes may converge towards some localized non-equilibrium steady state when the two velocities and/or the two switching rates are space-dependent. A long dynamical trajectory can be then analyzed via the…
In contrast to conservative systems, in nonlinear media with gain and loss the dynamics of localized topological structures can exhibit unique features that can be controlled externally. We propose a robust mechanism to perform topological…
We study analytically and by computer simulations a complex system of adaptive agents with finite memory. Borrowing the framework of the Minority Game and using the replica formalism we show the existence of an equilibrium phase transition…
Reliability analysis is a sub-field of uncertainty quantification that assesses the probability of a system performing as intended under various uncertainties. Traditionally, this analysis relies on deterministic models, where experiments…
Cyclic (rock-paper-scissors-type) population models serve to mimic complex species interactions. Focusing on a paradigmatic three-species model with mutations in one dimension, we observe an interplay between equilibrium and non-equilibrium…
In an adaptive population which models financial markets and distributed control, we consider how the dynamics depends on the diversity of the agents' initial preferences of strategies. When the diversity decreases, more agents tend to…
Computer simulations generate trajectories at a single, well-defined thermodynamic state point. Statistical reweighting offers the means to reweight static and dynamical properties to different equilibrium state points by means of analytic…
The time-dependent probability density function of a system evolving towards a stationary state exhibits an oscillatory behavior if the eigenvalues of the corresponding evolution operator are complex. The frequencies \omega_n, with which…
We present a computational pipe aiming at recovery of the topology of the underlying phase space from observation of an output function along a sample of trajectories of a dynamical system.
We show, by using direct numerical simulations and theory, how, by increasing the order of dissipativity ($\alpha$) in equations of hydrodynamics, there is a transition from a dissipative to a conservative system. This remarkable result,…
In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…
A calculational approach in fluid turbulence is presented. Use is made of the attracting nature of the fluid-dynamic dynamical system. An approach is offered that effectively propagates the statistics in time. Loss of sensitivity to an…
Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
By using straightforward frequency arguments we classify transformations of probabilities which can be generated by transition from one preparation procedure (context) to another. There are three classes of transformations corresponding to…
We propose a one-dimensional nonlinear system of coupled anharmonic oscillators that dynamically undergoes a topological transition switching from the {disordered} and topologically trivial phase into the nontrivial one due to the…