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Conserved dynamical systems are generally considered to be critical. We study a class of critical routing models, equivalent to random maps, which can be solved rigorously in the thermodynamic limit. The information flow is conserved for…
Systems of oscillators subject to time-dependent noise typically achieve synchronization for long times when their mutual coupling is sufficiently strong. The dynamical process whereby synchronization is reached can be thought of as a…
Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our…
Periodic driving is used to operate machines that go from standard macroscopic engines to small non-equilibrium micro-sized systems. Two classes of such systems are small heat engines driven by periodic temperature variations and molecular…
The paper is concerned with mechanical systems which are controlled by implementing a number of time-dependent, frictionless holonomic constraints. The main novelty is due to the presence of additional non-holonomic constraints. We develop…
Steady state fluctuation relations for dynamical systems are commonly derived under the assumption of some form of time-reversibility and of chaos. There are, however, cases in which they are observed to hold even if the usual notion of…
Subharmonic response is a well known phenomena in, e.g., deterministic nonlinear dynamical systems. We investigate the conditions under which such subharmonic oscillations can persist for a long time in open systems with stochastic dynamics…
A hybrid system is a system whose dynamics is given by a mixture of both continuous and discrete transitions. In particular, these systems can be utilised to describe the dynamics of a mechanical system with impacts. Based on the approach…
We study the problem of system identification for stochastic continuous-time dynamics, based on a single finite-length state trajectory. We present a method for estimating the possibly unstable open-loop matrix by employing properly…
One possible framework to interpret the irreversibility transition observed in periodically driven colloidal suspensions is that of a non-equilibrium phase transition towards an absorbing reversible state at low amplitude of the driving…
The synchronization of rhythms is ubiquitous in both natural and engineered systems, and the demand for data-driven analysis is growing. When rhythms arise from limit cycles, phase reduction theory shows that their dynamics are universally…
We study the collective behaviour of an ensemble of coupled motile elements whose interactions depend on time and are alternatively attractive or repulsive. The evolution of interactions is driven by individual internal variables with…
A (closed) dynamical system is a notion of how things can be, together with a notion of how they may change given how they are. The idea and mathematics of closed dynamical systems has proven incredibly useful in those sciences that can…
Natural dynamics is often dominated by sudden nonlinear processes such as neuroavalanches, gamma-ray bursts, solar flares \emph{etc}. that exhibit scale-free statistics much in the spirit of the logarithmic Ritcher scale for earthquake…
A variety of nonlinear models of biological systems generate complex chaotic behaviors that contrast with biological homeostasis, the observation that many biological systems prove remarkably robust in the face of changing external or…
We prove the holding of chaos in the sense of Li-Yorke for a family of four-dimensional discrete dynamical systems that are naturally associated to ODE systems describing coupled oscillators subject to an external non-conservative force,…
In this paper, a non-autonomous stochastic logistic system is considered. An interesting result on the effect of stochastically perturbation for the dynamic behavior are obtained. That is, under certain conditions the stochastic system have…
We develop a generalized stability framework for stochastic discrete-time systems, where the generality pertains to the ways in which the distribution of the state energy can be characterized. We use tools from finance and operations…
We develop a sound and complete graphical theory for discrete linear time-invariant dynamical systems. The graphical syntax, as in previous work, is closely related to the classical notion of signal flow diagrams, differently from previous…
Time crystals are classified into discrete time crystals and continuous time crystals based on whether they spontaneously break time-translation symmetry. Continuous-time crystals do not require external driving. By introducing AdS/CFT…