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In spatially distributed cellular systems, it is often convenient to represent complicated auxiliary pathways and spatial transport by time-delayed reaction rates. Furthermore, many of the reactants appear in low numbers necessitating a…
Explaining the wide range of dynamics observed in ecological communities is challenging due to the large number of species involved, the complex network of interactions among them, and the influence of multiple environmental variables.…
The long-term behaviour of dynamic systems can be classified in two different regimes, regular or chaotic, depending on the values of the control parameters, which are kept constant during the time evolution. Starting from slightly…
The stability of solutions to evolution equations with respect to small stochastic perturbations is considered. The stability of a stochastic dynamical system is characterized by the local stability index. The limit of this index with…
This is the transcript of a talk given at the 1992 Complex Systems Summer School. The theory of large fluctuations of stochastically perturbed continuous-time dynamical systems is reviewed, and the large fluctuations of two stochastic…
Random walks serve as important tools for studying complex network structures, yet their dynamics in cases where transition probabilities are not static remain under explored and poorly understood. Here we study nonlinear random walks that…
Stochastic storage models based on essentially non-Gaussian noise are considered. The stochastic description of physical systems based on stochastic storage models is associated with generalized Poisson (or shot) noise, in which the jump…
Whereas the importance of transient dynamics to the functionality and management of complex systems has been increasingly recognized, most of the studies are based on models. Yet in realistic situations the models are often unknown and what…
We investigate the time evolution process of one selected (initially prepared by optical pumping) vibrational molecular state, coupled to all other intra-molecular vibrational states of the same molecule, and also to its environment.…
High energy scattering was recently shown to be similar to a reaction-diffusion process. The latter defines a wide universality class that also contains e.g. some specific population evolution models. The common point of all these models is…
Dynamics is central to living systems. In the last two decades, experiments have revealed that the dynamics in diverse biological systems - from intracellular cytoplasm to cellular and organismal aggregates - are remarkably similar to that…
Catastrophes of all kinds can be roughly defined as short duration-large amplitude events following and followed by long periods of "ripening". Major earthquakes surely belong to the class of 'catastrophic' events. Because of the space-time…
We point out that in the first order time-dependent perturbation theory, the transition probability may behave nonsmoothly in time and have kinks periodically. Moreover, the detailed temporal evolution can be sensitive to the exact…
Populations of replicating entities frequently experience sudden or cyclical changes in environment. We explore the implications of this phenomenon via a environmental switching parameter in several common evolutionary dynamics models…
We start by reviewing recent probabilistic results on ergodic sums in a large class of (non-uniformly) hyperbolic dynamical systems. Namely, we describe the central limit theorem, the almost-sure convergence to the gaussian and other stable…
The nature and source of evolutionary trends in complexity is difficult to assess from the fossil record, and the driven vs. passive nature of such trends has been debated for decades. There are also questions about how effectively…
This paper attempts to make feasible the evolutionary emergence of novelty in a supposedly deterministic world which behavior is associated with those of the mathematical dynamical systems. The work was motivated by the observation of…
Mathematical models of real life phenomena are highly nonlinear involving multiple parameters and often exhibiting complex dynamics. Experimental data sets are typically small and noisy, rendering estimation of parameters from such data…
We analyze a class of dynamics of open quantum systems which is governed by the dynamical map mutually commuting at different times. Such evolution may be effectively described via spectral analysis of the corresponding time dependent…
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…