Related papers: Basins of Attraction: A Dynamical Zoo
Attractor dynamics are a fundamental computational motif in neural circuits, supporting diverse cognitive functions through stable, self-sustaining patterns of neural activity. In these lecture notes, we review four key examples that…
The paper considers some class of dynamical systems that called density systems. For such systems the derivative of quadratic function depends on so-called density function. The density function is used to set the properties of phase space,…
To explore basin geometry in high-dimensional dynamical systems, we consider a ring of identical Kuramoto oscillators. Many attractors coexist in this system; each is a twisted periodic orbit characterized by a winding number $q$, with…
In the paper arguments are given why the concept of static evaluation has the potential to be a useful extension to Monte Carlo tree search. A new concept of modeling static evaluation through a dynamical system is introduced and strengths…
Cosmology is a well established research area in physics while dynamical systems are well established in mathematics. It turns out that dynamical system techniques are very well suited to study many aspects of cosmology. The aim of this…
This research proposes new tools for investigation of behavioral diversity in multi-robot systems and a significant body of results using these tools in simulated and real mobile robot experiments. The experiments specifically describe a…
We report a study of the basins of attraction for potential energy minima defined by different minimisation algorithms for an atomic system. We find that whereas some minimisation algorithms produce compact basins, others produce basins…
This paper establishes a general framework for describing hybrid dynamical systems which is particularly suitable for numerical simulation. In this context, the data structures used to describe the sets and functions which comprise the…
Because of consuming energy to drive their motion, systems of active colloids are intrinsically out of equilibrium. In the past decade, a variety of intriguing dynamic patterns have been observed in systems of active colloids, and they…
A stochastic dynamics framework for the study of complex systems is presented.
Habituation - a phenomenon in which a dynamical system exhibits a diminishing response to repeated stimulations that eventually recovers when the stimulus is withheld - is universally observed in living systems from animals to unicellular…
Stability and analysis of multi-agent network systems with state-dependent switching typologies have been a fundamental and longstanding challenge in control, social sciences, and many other related fields. These already complex systems…
Network science has become an essential interdisciplinary tool for understanding complex biological systems. However, because these systems undergo continuous, often stimulus-driven changes in both structure and function, traditional static…
Despite their deterministic nature, dynamical systems often exhibit seemingly random behaviour. Consequently, a dynamical system is usually represented by a probabilistic model of which the unknown parameters must be estimated using…
Bistability is a ubiquitous phenomenon in life sciences. In this paper, two kinds of bistable structures in dynamical systems are studied: One is two one-point attractors, another is a one-point attractor accompanied by a cycle attractor.…
In a complex system, the individual components are neither so tightly coupled or correlated that they can all be treated as a single unit, nor so uncorrelated that they can be approximated as independent entities. Instead, patterns of…
Our society is digital: industry, science, governance, and individuals depend, often transparently, on the inter-operation of large numbers of distributed computer systems. Although the society takes them almost for granted, these computer…
This paper argues that continual learning methods can benefit by splitting the capacity of the learner across multiple models. We use statistical learning theory and experimental analysis to show how multiple tasks can interact with each…
Many animals live in societies where individuals frequently interact socially with each other. The social structures of these systems can be studied in depth by means of network analysis. A large number of studies on animal social networks…
We propose dynamical systems trees (DSTs) as a flexible class of models for describing multiple processes that interact via a hierarchy of aggregating parent chains. DSTs extend Kalman filters, hidden Markov models and nonlinear dynamical…