3,167 research outputs found
Modelling chemotaxis of microswimmers: from individual to collective behavior
We discuss recent progress in the theoretical description of chemotaxis by
coupling the diffusion equation of a chemical species to equations describing
the motion of sensing microorganisms. In particular, we discuss models for
autochemotaxis of a single microorganism which senses its own secretion leading
to phenomena such as self-localization and self-avoidance. For two
heterogeneous particles, chemotactic coupling can lead to predator-prey
behavior including chase and escape phenomena, and to the formation of active
molecules, where motility spontaneously emerges when the particles approach
each other. We close this review with some remarks on the collective behavior
of many particles where chemotactic coupling induces patterns involving
clusters, spirals or traveling waves.Comment: to appear as a contribution to the book "Chemical kinetics beyond the
textbook
Field-theoretic methods
Many complex systems are characterized by intriguing spatio-temporal
structures. Their mathematical description relies on the analysis of
appropriate correlation functions. Functional integral techniques provide a
unifying formalism that facilitates the computation of such correlation
functions and moments, and furthermore allows a systematic development of
perturbation expansions and other useful approximative schemes. It is explained
how nonlinear stochastic processes may be mapped onto exponential probability
distributions, whose weights are determined by continuum field theory actions.
Such mappings are madeexplicit for (1) stochastic interacting particle systems
whose kinetics is defined through a microscopic master equation; and (2)
nonlinear Langevin stochastic differential equations which provide a mesoscopic
description wherein a separation of time scales between the relevant degrees of
freedom and background statistical noise is assumed. Several well-studied
examples are introduced to illustrate the general methodology.Comment: Article for the Encyclopedia of Complexity and System Science, B.
Meyers (Ed.), Springer-Verlag Berlin, 200
Spatio-temporal stochastic resonance induces patterns in wetland vegetation dynamics
Water availability is a major environmental driver affecting riparian and
wetland vegetation. The interaction between water table fluctuations and
vegetation in a stochastic environment contributes to the complexity of the
dynamics of these ecosystems. We investigate the possible emergence of spatial
patterns induced by spatio-temporal stochastic resonance in a simple model of
groundwater-dependent ecosystems. These spatio-temporal dynamics are driven by
the combined effect of three components: (i) an additive white Gaussian noise,
accounting for external random disturbances such as fires or fluctuations in
rain water availability, (ii) a weak periodic modulation in time, describing
hydrological drivers such as seasonal fluctuations of water table depth, and
(iii) a spatial coupling term, which takes into account the ability of
vegetation to spread and colonize other parts of the landscape. A suitable
cooperation between these three terms is able to give rise to ordered
structures which show spatial and temporal coherence, and are statistically
steady in time.Comment: 9 pages, 7 figure
Deterministic continutation of stochastic metastable equilibria via Lyapunov equations and ellipsoids
Numerical continuation methods for deterministic dynamical systems have been
one of the most successful tools in applied dynamical systems theory.
Continuation techniques have been employed in all branches of the natural
sciences as well as in engineering to analyze ordinary, partial and delay
differential equations. Here we show that the deterministic continuation
algorithm for equilibrium points can be extended to track information about
metastable equilibrium points of stochastic differential equations (SDEs). We
stress that we do not develop a new technical tool but that we combine results
and methods from probability theory, dynamical systems, numerical analysis,
optimization and control theory into an algorithm that augments classical
equilibrium continuation methods. In particular, we use ellipsoids defining
regions of high concentration of sample paths. It is shown that these
ellipsoids and the distances between them can be efficiently calculated using
iterative methods that take advantage of the numerical continuation framework.
We apply our method to a bistable neural competition model and a classical
predator-prey system. Furthermore, we show how global assumptions on the flow
can be incorporated - if they are available - by relating numerical
continuation, Kramers' formula and Rayleigh iteration.Comment: 29 pages, 7 figures [Fig.7 reduced in quality due to arXiv size
restrictions]; v2 - added Section 9 on Kramers' formula, additional
computations, corrected typos, improved explanation
Red Queen Coevolution on Fitness Landscapes
Species do not merely evolve, they also coevolve with other organisms.
Coevolution is a major force driving interacting species to continuously evolve
ex- ploring their fitness landscapes. Coevolution involves the coupling of
species fit- ness landscapes, linking species genetic changes with their
inter-specific ecological interactions. Here we first introduce the Red Queen
hypothesis of evolution com- menting on some theoretical aspects and empirical
evidences. As an introduction to the fitness landscape concept, we review key
issues on evolution on simple and rugged fitness landscapes. Then we present
key modeling examples of coevolution on different fitness landscapes at
different scales, from RNA viruses to complex ecosystems and macroevolution.Comment: 40 pages, 12 figures. To appear in "Recent Advances in the Theory and
Application of Fitness Landscapes" (H. Richter and A. Engelbrecht, eds.).
Springer Series in Emergence, Complexity, and Computation, 201
Predator-prey survival pressure is sufficient to evolve swarming behaviors
The comprehension of how local interactions arise in global collective
behavior is of utmost importance in both biological and physical research.
Traditional agent-based models often rely on static rules that fail to capture
the dynamic strategies of the biological world. Reinforcement learning has been
proposed as a solution, but most previous methods adopt handcrafted reward
functions that implicitly or explicitly encourage the emergence of swarming
behaviors. In this study, we propose a minimal predator-prey coevolution
framework based on mixed cooperative-competitive multiagent reinforcement
learning, and adopt a reward function that is solely based on the fundamental
survival pressure, that is, prey receive a reward of if caught by
predators while predators receive a reward of . Surprisingly, our analysis
of this approach reveals an unexpectedly rich diversity of emergent behaviors
for both prey and predators, including flocking and swirling behaviors for
prey, as well as dispersion tactics, confusion, and marginal predation
phenomena for predators. Overall, our study provides novel insights into the
collective behavior of organisms and highlights the potential applications in
swarm robotics
Biodiversity in model ecosystems, I: Coexistence conditions for competing species
This is the first of two papers where we discuss the limits imposed by
competition to the biodiversity of species communities. In this first paper we
study the coexistence of competing species at the fixed point of population
dynamic equations. For many simple models, this imposes a limit on the width of
the productivity distribution, which is more severe the more diverse the
ecosystem is (Chesson, 1994). Here we review and generalize this analysis,
beyond the ``mean-field''-like approximation of the competition matrix used in
previous works, and extend it to structured food webs. In all cases analysed,
we obtain qualitatively similar relations between biodiversity and competition:
the narrower the productivity distribution is, the more species can stably
coexist. We discuss how this result, considered together with environmental
fluctuations, limits the maximal biodiversity that a trophic level can host
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