Related papers: Dynamics with choice
Cells move differently on substrates with different elasticities. In particular, the persistence time of their motion is higher on stiffer substrates. We show that this behavior will result in a net transport of cells directed up a…
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…
The qualitative study of dynamical systems using bifurcation theory is key to understanding systems from biological clocks and neurons to physical phase transitions. Data generated from such systems can feature complex transients, an…
We study the evolution of observables of dynamical systems. For linear systems, we show that observables satisfy a closed differential equation whose minimal order is determined by the dynamical system and observation operator. This yields…
Biological evolution of a population is governed by the fitness landscape, which is a map from genotype to fitness. However, a fitness landscape depends on the organisms environment, and evolution in changing environments is still poorly…
An open problem in numerical analysis is to explain why molecular dynamics works. The difficulty is that numerical trajectories are only accurate for very short times, whereas the simulations are performed over long time intervals. It is…
Since its inception, the choice modelling field has been dominated by theory-driven modelling approaches. Machine learning offers an alternative data-driven approach for modelling choice behaviour and is increasingly drawing interest in our…
A general system of particles (of one or several species) on a one dimensional lattice with boundaries is considered. Two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the…
Mathematical models are vital interpretive and predictive tools used to assist in the understanding of cell migration. There are typically two approaches to modelling cell migration: either micro-scale, discrete or macro-scale, continuum.…
Our understanding of evolution is shaped strongly by how we conceive of its fundamental causes. In the original Modern Synthesis, evolution was defined as a process of shifting the frequencies of available alleles at many loci affecting a…
Chaos is an active research subject in the fields of science in recent years. it is a complex and an erratic behavior that is possible in very simple systems. in the present day, the chaotic behavior can be observed in experiments. Many…
This article shows how to specify and construct a discrete, stochastic, continuous-time model specifically for ecological systems. The model is more broad than typical chemical kinetics models in two ways. First, using time-dependent hazard…
The probabilistic description of the time evolution of a physical system can take two conceptually distinct forms: a trajectory of probabilities, which specifies how probabilities evolve over time, and a probability on trajectories, which…
We are living in an uncertain and dynamically changing world, where optimal decision-making under uncertainty is directly linked to the survival of species. However, evolutionary selection pressures that shape value-based decision-making…
Cooperation is a difficult proposition in the face of Darwinian selection. Those that defect have an evolutionary advantage over cooperators who should therefore die out. However, spatial structure enables cooperators to survive through the…
Understanding the evolution of cooperation is pivotal in biology and social science. Public resources sharing is a common scenario in the real world. In our study, we explore the evolutionary dynamics of cooperation on a regular graph with…
The emergence and decline of democratic systems worldwide raises fundamental questions about the dynamics of political change. Contrary to the idea of a stable endpoint of liberal democracy, recent backsliding towards less democratic…
Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics…
Dynamical sampling deals with signals that evolve in time under the action of a linear operator. The purpose of the present paper is to analyze the performance of the basic dynamical sampling algorithms in the finite dimensional case and…
Organisms and ecological groups accumulate evidence to make decisions. Classic experiments and theoretical studies have explored this process when the correct choice is fixed during each trial. However, we live in a constantly changing…