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Reaction-diffusion systems have been proposed as a model for pattern formation and morphogenesis. The Fickian diffusion typically employed in these constructions model the Brownian motion of particles. The biological and chemical elements…
The emerging collective motions of swarms of interacting agents are a subject of great interest in application areas ranging from biology to physics and robotics. In this paper, we conduct a careful analysis of the collective dynamics of a…
From flocking birds to schooling fish, organisms interact to form collective dynamics across the natural world. Self-organization is present at smaller scales as well: cells interact and move during development to produce patterns in fish…
Spatial patterns are widely observed in numerous nonequilibrium natural systems, often undergoing complex transitions and bifurcations, thereby exhibiting significant importance in many physical and biological systems such as embryonic…
This paper describes a framework for the investigation and modeling of human spatial guidance behavior in complex environments. The model is derived from the concept of interaction patterns, which represent the invariances or symmetries…
Spatial patterning is common in ecological systems and has been extensively studied via different modeling approaches. Individual-based models (IBMs) accurately describe nonlinear interactions at the organism level and the stochastic…
We consider a reaction-diffusion model for a population structured in phenotype. We assume that the population lives in a heterogeneous periodic environment, so that a given phenotypic trait may be more or less fit according to the spatial…
Swarming behavior, where coherent motion emerges from the interactions of many mobile agents, is ubiquitous in physics and biology. Moreover, there are many efforts to replicate swarming dynamics in mobile robotic systems which take…
We discuss biologically inspired, inherently non-equilibrium self-propelled particle models, in which the particles interact with their neighbours by choosing at each time step the local average direction of motion. We summarize some of the…
In many natural synchronization phenomena, communication between individual elements occurs not directly, but rather through the environment. One of these instances is bacterial quorum sensing, where bacteria release signaling molecules in…
The symbiotic branching model describes the dynamics of a spatial two-type population, where locally particles branch at a rate given by the frequency of the other type combined with nearest-neighbour migration. This model generalizes…
Alignment interactions in active matter are typically modeled as relaxational dynamics toward local consensus. In unbounded systems, this makes alignment effectively decoupled from local density and therefore unable to sustain self-confined…
Bacteria can form a great variety of spatially heterogeneous cell density patterns, ranging from simple concentric rings to dynamical spiral waves appearing in growing colonies. These pattern formation phenomena are important as they…
Sustained rhythmic oscillations, pulsing dynamics, emerge spontaneously when the local connection scheme is randomised in 3-value cellular automata that feature"glider" dynamics. Time-plots of pulsing measures maintain a distinct waveform…
Many real-world systems can be modeled as networks of interacting oscillatory units. Collective dynamics that are of functional relevance for the oscillator network, such as switching between metastable states, arise through the interplay…
Face-to-face interaction networks describe social interactions in human gatherings, and are the substrate for processes such as epidemic spreading and gossip propagation. The bursty nature of human behavior characterizes many aspects of…
Nonequilibrium membrane pattern formation is studied using meshless membrane simulation. We consider that molecules bind to either surface of a bilayer membrane and move to the opposite leaflet by flip--flop. When binding does not modify…
In this paper, we study a single-species population model with pulse toxicant input to a small polluted environment. The intrinsic rate of population is affected by environment and toxin in organisms. The toxin in organisms is influenced by…
Numerical simulations of a simple reaction--diffusion model reveal a surprising variety of irregular spatio--temporal patterns. These patterns arise in response to finite--amplitude perturbations. Some of them resemble the steady irregular…
Stochastic modeling of disease dynamics has had a long tradition. Among the first epidemic models including a spatial structure in the form of local interactions is the contact process. In this article we investigate two extensions of the…