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The effect of disturbance on a model ecosystem of sessile and mutually competitive species [Mathiesen et al. Phys. Rev. Lett. 107, 188101 (2011); Mitarai et al. Phys. Rev. E 86, 011929 (2012) ] is studied. The disturbance stochastically…
Multi-Agent Reinforcement Learning involves agents that learn together in a shared environment, leading to emergent dynamics sensitive to initial conditions and parameter variations. A Dynamical Systems approach, which studies the evolution…
Voltage stability in modern power systems involves coupled dynamics across multiple time scales. Conventional methods based on time-scale separation or static stability margins may overlook instabilities caused by the coupling of slow and…
The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…
Real systems are usually composed by units or nodes whose activity can be interrupted and restored intermittently due to complex interactions not only with the environment, but also with the same system. Majdand\v{z}i\'c $et\;al.$ [Nature…
Various functions of a network of excitable units can be enhanced if the network is in the `critical regime', where excitations are, on average, neither damped nor amplified. An important question is how can such networks self-organize to…
Estimating the effective energy, $E_\text{eff}$ of a stationary probability distribution is a challenge for non-equilibrium steady states. Its solution could offer a novel framework for describing and analyzing non-equilibrium systems. In…
Complementarity is one of the main features underlying the interactions in biological and biochemical systems. Inspired by those systems we propose a model for the dynamical evolution of a system composed by agents that interact due to…
Temporal modulation of components of electromagnetic systems provides an exceptional opportunity to engineer the response of those systems in a desired fashion, both in the time and frequency domains. For engineering time-modulated systems,…
Deriving emergent patterns from models of biological processes is a core concern of mathematical biology. In the context of partial differential equations (PDEs), these emergent patterns sometimes appear as local minimisers of a…
Topological phases support edge states that can be robust to material deformations and other perturbations. While well-studied in quantum systems, topological phases have also been observed in stochastic and biochemical systems, yet it…
Networks of globally coupled, noise activated, bistable elements with connection time delays are considered. The dynamics of these systems is studied numerically using a Langevin description and analytically using (1) a Gaussian…
Nearly-elastic model systems with one or two degrees of freedom are considered: the system is undergoing a small loss of energy in each collision with the "wall". We show that instabilities in this purely deterministic system lead to…
Bias plays an important role in the enhancement of diffusion in periodic potentials. Using the continuous-time random walk in the presence of a bias, we provide a novel mechanism for the enhancement of diffusion in a random energy…
This paper provides a comprehensive analysis of stability and long-time behaviour of a coupled system constituted by two rigid bodies separated by a thin layer of lubricant. We show that permanent rotations of the whole system, with the…
Topological concepts have been employed to understand the ground states of many strongly correlated systems, but it is still quite unclear if and how topology manifests itself in the relaxation dynamics. Here we uncover emergent topological…
The emergence and evolution of real-world systems have been extensively studied in the last few years. However, equally important phenomena are related to the dynamics of systems' collapse, which has been less explored, especially when they…
In this work, we introduce the Time-Aware World Model (TAWM), a model-based approach that explicitly incorporates temporal dynamics. By conditioning on the time-step size, {\Delta}t, and training over a diverse range of {\Delta}t values --…
We study the dynamics of a collection of nonlinearly coupled limit cycle oscillators, relevant to systems ranging from neuronal populations to electrical circuits, under coupling topologies varying from a regular ring to a random network.…
Stochastic models such as Continuous-Time Markov Chains (CTMC) and Stochastic Hybrid Automata (SHA) are powerful formalisms to model and to reason about the dynamics of biological systems, due to their ability to capture the stochasticity…