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We introduce a stochastic agent-based model for the flocking dynamics of self-propelled particles that exhibit velocity-alignment interactions with neighbours within their field of view. The stochasticity in the dynamics of the model arises…
A mean-field selective optimal control problem of multipopulation dynamics via transient leadership is considered. The agents in the system are described by their spatial position and their probability of belonging to a certain population.…
Fluctuating environments are situations where the spatio-temporal stochasticity plays a significant role in the evolutionary dynamics. The study of the evolution of cooperation in these environments typically assumes a homogeneous, well…
Complex change is often described as "evolutionary" in economics, policy, and technology, yet most system dynamics models remain constrained to fixed state spaces and equilibrium-seeking behavior. This paper argues that evolutionary…
Populations evolving under the joint influence of recombination and resampling (traditionally known as genetic drift) are investigated. First, we summarise and adapt a deterministic approach, as valid for infinite populations, which assumes…
Due to the conventional distinction between ecological (rapid) and evolutionary (slow)timescales, ecological and population models to date have typically ignored the effects of evolution. Yet the potential for rapid evolutionary change has…
Understanding systems level behaviour of many interacting agents is challenging in various ways, here we'll focus on the how the interaction between components can lead to hierarchical structures with different types of dynamics, or…
To traverse complex three-dimensional terrainwith large obstacles, animals and robots must transition across different modes. However, the most mechanistic understanding of terrestrial locomotion concerns how to generate and stabilize…
The Moran process is a classic stochastic process that models invasion dynamics on graphs. A single "mutant" (e.g., a new opinion, strain, social trait etc.) invades a population of residents spread over the nodes of a graph. The mutant…
The emergence of collective cooperation in competitive environments is a well-known phenomenon in biology, economics, and social systems. While most evolutionary game models focus on the evolution of strategies for a fixed game, how…
Stochastic diffusion is the noisy and uncertain process through which dynamics like epidemics, or agents like animal species, disperse over a larger area. Understanding these processes is becoming increasingly important as we attempt to…
Cooperation is ubiquitous across all levels of biological systems ranging from microbial communities to human societies. It, however, seemingly contradicts the evolutionary theory, since cooperators are exploited by free-riders and thus are…
This paper develops and analyzes a diffusion-advection model coupling population dynamics with toxicant transport, incorporating a boundary protection zone. For both upstream and downstream protection zone configurations, we investigate the…
Under the effects of strong genetic drift, it is highly probable to observe gene fixation or loss in a population, shown by divergent probability density functions, or infinite adaptive peaks on a landscape. It is then interesting to ask…
We study the distribution of traffic in networks whose users try to minimise their delays by adhering to a simple learning scheme inspired by the replicator dynamics of evolutionary game theory. The stable steady states of these dynamics…
Multi-Agent Reinforcement Learning involves agents that learn together in a shared environment, leading to emergent dynamics sensitive to initial conditions and parameter variations. A Dynamical Systems approach, which studies the evolution…
How diversity is maintained in natural ecosystems is a long-standing question in Theoretical Ecology. By studying a system that combines ecological dynamics, heterogeneous interactions and spatial structure, we uncover a new mechanism for…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…
Biodiversity and extinction are central issues in evolution. Dynamical balance among different species in ecosystems is often described by deterministic replicator equations with moderate success. However, fluctuations are inevitable,…
Consider a mathematical model of evolutionary adaptation of fitness landscape and mutation matrix as a reaction to population changes. As a basis, we use an open quasispecies model, which is modified to include explicit death flow. We…