Related papers: Towards a unified framework for multiple stable st…
Evolutionary game theory has been successfully used to investigate the dynamics of systems, in which many entities have competitive interactions. From a physics point of view, it is interesting to study conditions under which a coordination…
In this paper, we discuss various topological and metrical aspects of the set of stabilizing static feedback gains for multiple-input-multiple-output (MIMO) linear-time-invariant (LTI) systems, in both continuous and discrete-time.…
We introduce a Hamiltonian dynamics for the description of long-range interacting systems in contact with a thermal bath (i.e., in the canonical ensemble). The dynamics confirms statistical mechanics equilibrium predictions for the…
Tipping elements in the climate system are large-scale subregions of the Earth that might possess threshold behavior under global warming with large potential impacts on human societies. Here, we study a subset of five tipping elements and…
Models in evolutionary game theory traditionally assume symmetric interactions in homogeneous environments. Here, we consider populations evolving in a heterogeneous environment, which consists of patches of different qualities that are…
We analyst in detail a new approach to the monitoring and forecasting of the onset of transitions in high dimensional complex systems (see Phys. Rev. Lett . vol. 113, 264102 (2014)) by application to the Tangled Nature Model of evolutionary…
Interconnected networks describe the dynamics of important systems in a wide range such as biological systems and electrical power grids. Some important features of these systems were successfully studied and understood through simplified…
The key feature of a quantum spin coupled to a harmonic bath---a model dissipative quantum system---is competition between oscillator potential energy and spin tunneling rate. We show that these opposing tendencies cause environmental…
Feedback loops are major components of biochemical systems. Many systems show multiple such (positive or negative) feedback loops. Nevertheless, very few quantitative analyses address the question how such multiple feedback loops evolved.…
We study the evolutionary dynamics of games under environmental feedback using replicator equations for two interacting populations. One key feature is to consider jointly the co-evolution of the dynamic payoff matrices and the state of the…
We investigate species-rich mathematical models of ecosystems. While much of the existing literature focuses on the properties of equilibrium fixed points, persistent dynamics (e.g., limit cycles or chaos) have also been observed, both in…
We propose a methodology to analyze synchronization in an ensemble of diffusively coupled multistable systems. First, we study how two bidirectionally coupled multistable oscillators synchronize and demonstrate the high complexity of the…
Single-loop elastic rings can be folded into multi-loop equilibrium configurations. In this paper, the stability of several such multi-loop states which are either circular or straight are investigated analytically and illustrated by…
We present new theoretical and empirical results on the probability distributions of species persistence times in natural ecosystems. Persistence times, defined as the timespans occurring between species' colonization and local extinction…
A model is proposed that describes the evolution of a mixed state of a quantum system for which gain and loss of energy or amplitude are present. Properties of the model are worked out in detail. In particular, invariant subspaces of the…
Ecosystems are formed by networks of species and their interactions. Traditional models of such interactions assume a constant interaction strength between a given pair of species. However, there is often significant trait variation among…
Mutualistic interactions, where individuals from different species can benefit from each other, are widespread across ecosystems. This study develops a general deterministic model of mutualism involving two populations, assuming that…
We explore the stability properties of multi-field solutions of assisted inflation type, where several fields collectively evolve to the same configuration. In the case of noninteracting fields, we show that the condition for such solutions…
We study the dynamics of lattice models of quantum spins one-half, driven by a coherent drive and subject to dissipation. Generically the meanfield limit of these models manifests multistable parameter regions of coexisting steady states…
In this paper we return to the problem of reduced-state dynamics in the presence of an interacting environment. The question we investigate is how to appropriately model a particular system evolution given some knowledge of the…