Related papers: The road to catastrophe: stability and collapse in…
We model the dynamics of social structure by a simple interacting particle system. The social standing of an individual agent is represented by an integer-valued fitness that changes via two offsetting processes. When two agents interact…
In the first half of the paper, some recent advances in coupled dynamical systems, in particular, a globally coupled map are surveyed. First, dominance of Milnor attractors in partially ordered phase is demonstrated. Second, chaotic…
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…
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
This paper deals with the kinetic theory modeling of crowd dynamics with the aim of showing how the dynamics at the micro-scale is transferred to the dynamics of collective behaviors. The derivation of a new model is followed by a…
When particles move at a constant speed and have the tendency to align their directions of motion, ordered large scale movement can emerge despite significant levels of noise. Many variants of this model of self-propelled particles have…
The theory, the design and the experimental validation of a catastrophe machine based on a flexible element are addressed for the first time. A general theoretical framework is developed by extending that of the classical catastrophe…
Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems like the power grid, social, and neural networks, and they form the…
Natural flocks (aligned) and swarms (non-aligned) both exhibit features of near-criticality, challenging their treatment as two ends of the same phase transition. We present a model for the aggregation of active individuals, in which their…
We investigate a system of co-oriented active particles interacting only via hydrodynamic and steric interactions. We offer a new method of calculating the flow created by any active particle in a 2D fluid, focusing on the dynamics of flow…
A microscopic, stochastic, minimal model for collective and cohesive motion of identical self-propelled particles is introduced. Even though the particles interact strictly locally in a very noisy manner, we show that cohesion can be…
Our recent interest is focused on establishing the necessary and sufficient conditions that guarantee a long-term stable evolution of both natural and artificial systems. Two necessary conditions, called global and local boundedness, are…
We use computer simulations to study the onset of collective motion in systems of interacting active particles. Our model is a swarm of active Brownian particles with internal energy depot and interactions inspired by the dissipative…
In recent years statistical physicists have developed {\it discrete} "particle-hopping" models of vehicular traffic, usually formulated in terms of {\it cellular automata}, which are similar to the microscopic models of interacting charged…
The state of a classical point-particle system may often be specified by giving the position and momentum for each constituent particle. For non-pointlike particles, the center-of-mass position may be augmented by an additional coordinate…
New features related to collective properties generated in the systems driven by random dynamics are observed and their implications for further understanding of interplay between coherence and chaos are discussed.
A microscopic field theory for crystallization in active systems is proposed which unifies the phase-field-crystal model of freezing with the Toner-Tu theory for self-propelled particles. A wealth of different active crystalline states are…
In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics…
We propose a novel approach in the study of transport phenomena in dense systems or systems with long range interactions where multiple particle interactions must be taken into consideration. Within Boltzmann's kinetic formalism, we study…