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A dynamical systems scenario for developmental cell biology is proposed, based on numerical studies of a system with interacting units with internal dynamics and reproduction. Diversification, formation of discrete and recursive types, and…
Recurrent neural policies are widely used in partially observable control and meta-RL tasks. Their abilities to maintain internal memory and adapt quickly to unseen scenarios have offered them unparalleled performance when compared to…
Multivariate oscillatory signals from complex systems often exhibit non-stationary dynamics and metastable regime structure, making dynamical interpretation challenging. We introduce a ``dynamical microscope'' framework that converts…
The traditional dynamical phase transition refers to the appearance of singularities in an observable with respect to a control parameter for a late-time state or singularities in the rate function of the Loschmidt echo with respect to…
We here describe the possibility of a synthetic description of the onset of Chaos in many degrees of freedom dynamical systems within the framework of the geometric description of dynamics. We show how this approach to instability helps to…
This chapter is dedicated to the slow dynamics of the climate system, at time scales of one~thousand to one million years. We focus specifically on the phenomenon of ice ages that has characterised the slow evolution of climate over the…
This work advances the theoretical foundations of reservoir computing (RC) by providing a unified treatment of fading memory and the echo state property (ESP) in both deterministic and stochastic settings. We investigate state-space…
Logarithmic aging phenomena are prevalent in various systems, including electronic materials and biological structures. This study utilizes a generalized continuous time random walk (CTRW) framework to investigate the mechanisms behind the…
Force-based models describe pedestrian dynamics in analogy to classical mechanics by a system of second order ordinary differential equations. By investigating the linear stability of two main classes of forces, parameter regions with…
Two properties of a dynamical system, rigidity and non-recurrence, are examined in detail. The ultimate aim is to characterize the sequences along which these properties do or do not occur for different classes of transformations. The main…
Transport in disordered media is a central theme in probability and statistical physics, where randomness in the underlying medium produces phenomena such as localization, anomalous scaling, and slow relaxation. A paradigmatic model for…
We study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong…
A general system of particles (of one or several species) on a one dimensional lattice with boundaries is considered. Two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the…
A general class of stochastic gene expression models with self regulation is considered. One or more genes randomly switch between regulatory states, each having a different mRNA transcription rate. The gene or genes are self regulating…
Recent work on stochastic interacting particle systems with two particle species (or single-species systems with kinematic constraints) has demonstrated the existence of spontaneous symmetry breaking, long-range order and phase coexistence…
The discrete stochastic dynamics of a random walker in the presence of resetting and memory is analyzed. Resetting and memory effects may compete for certain parameter regime and lead to significant changes in the long time dynamics of the…
Bursty dynamics is a common temporal property of various complex systems in Nature but it also characterises the dynamics of human actions and interactions. At the phenomenological level it is a feature of all systems that evolve…
By generalising concepts from classical stochastic dynamics, we establish the basis for a theory of metastability in Markovian open quantum systems. Partial relaxation into long-lived metastable states - distinct from the asymptotic…
In the theory of random dynamical systems (RDS), individuals with different initial states follow a same law of motion that is stochastically changing with time | called extrinsic noise. In the present work, intrin- sic noises for each…
We analyse metastable states in the East model, using a recently-proposed patch-repetition analysis based on time-averaged density profiles. The results reveal a hierarchy of states of varying lifetimes, consistent with previous studies in…