Related papers: Basins of Attraction: A Dynamical Zoo

Complex systems are characterized by many interacting units that give rise to emergent behavior. A particularly advantageous way to study these systems is through the analysis of the networks that encode the interactions among the system's…

We construct a class of quantum stochastic models of reservoir driven many-particle systems that are the natural counterparts of certain extensively studied classical ones, which have been shown to exhibit good hydrodynamical behaviour. Our…

We give a tutorial for the study of dynamical systems on networks. We focus especially on "simple" situations that are tractable analytically, because they can be very insightful and provide useful springboards for the study of more…

Artificial swarm systems have been extensively studied and used in computer science, robotics, engineering and other technological fields, primarily as a platform for implementing robust distributed systems to achieve pre-defined…

Metastability, characterized by a variability of regimes in time, is a ubiquitous type of neural dynamics. It has been formulated in many different ways in the neuroscience literature, however, which may cause some confusion. In this…

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…

All interesting and fascinating collective properties of a complex system arise from the intricate way in which its components interact. Various systems in physics, biology, social sciences and engineering have been successfully modelled as…

We calculate the period of recurrence of dynamical systems comprising two interacting bosons. A number of theoretical issues related to this problem are discussed, in particular, the conditions for small periodicity. The knowledge gathered…

We consider some planar triangular maps. These maps preserve certain fibration of the plane. We assume that there exists an invariant attracting fiber and we study the limit dynamics of those points in the basin of attraction of this…

First conceived as a topological construction, Wada basins abound in dynamical systems. Basins of attraction showing the Wada property possess the particular feature that any small perturbation of an initial condition lying on the boundary…

The review presents a parameter switching algorithm and his applications which allows numerical approximation of any attractor of a class of continuous-time dynamical systems depending linearly on a real parameter. The considered classes of…

Stochastic dynamic models have been extensively used for the description of processes with uncertainties arising in the operations research, behavioral sciences, and many other application areas. A large class of the problems from these…

Group behavior has received much attention as a test case of self-organization. There has been much written in recent years to investigate interactions within groups of agents. These agents can be animals moving in an interactive way, such…

Reservoir computing is a machine learning approach that can generate a surrogate model of a dynamical system. It can learn the underlying dynamical system using fewer trainable parameters and hence smaller training data sets than competing…

The deterministic dynamics of randomly connected neural networks are studied, where a state of binary neurons evolves according to a discreet-time synchronous update rule. We give a theoretical support that the overlap of systems' states…

The dynamics by iteration of a function on a compact metric space, sometimes called a cascade, can be extended to the dynamics of a closed relation on such a space. Here we apply this relation dynamics to study semiflows (and their relation…

A central feature of complex systems is the relevance and entanglement of different levels of description. For instance, the dynamics of ecosystems can be alternatively described in terms of large ecological processes and classes of…

Locomotion in the real world involves unexpected perturbations, and therefore requires strategies to maintain stability to successfully execute desired behaviours. Ensuring the safety of locomoting systems therefore necessitates a…

System identification of complex and nonlinear systems is a central problem for model predictive control and model-based reinforcement learning. Despite their complexity, such systems can often be approximated well by a set of linear…

We investigate the self-organising behaviour of Digital Ecosystems, because a primary motivation for our research is to exploit the self-organising properties of biological ecosystems. We extended a definition for the complexity, grounded…