142 research outputs found
Noise in ecosystems: a short review
Noise, through its interaction with the nonlinearity of the living systems,
can give rise to counter-intuitive phenomena such as stochastic resonance,
noise-delayed extinction, temporal oscillations, and spatial patterns. In this
paper we briefly review the noise-induced effects in three different
ecosystems: (i) two competing species; (ii) three interacting species, one
predator and two preys, and (iii) N-interacting species. The transient dynamics
of these ecosystems are analyzed through generalized Lotka-Volterra equations
in the presence of multiplicative noise, which models the interaction between
the species and the environment. The interaction parameter between the species
is random in cases (i) and (iii), and a periodical function, which accounts for
the environmental temperature, in case (ii). We find noise-induced phenomena
such as quasi-deterministic oscillations, stochastic resonance, noise-delayed
extinction, and noise-induced pattern formation with nonmonotonic behaviors of
patterns areas and of the density correlation as a function of the
multiplicative noise intensity. The asymptotic behavior of the time average of
the \emph{} population when the ecosystem is composed of a great number
of interacting species is obtained and the effect of the noise on the
asymptotic probability distributions of the populations is discussed.Comment: 27 pages, 16 figures. Accepted for publication in Mathematical
Biosciences and Engineerin
Noise Induced Phenomena in the Dynamics of Two Competing Species
Noise through its interaction with the nonlinearity of the living systems can
give rise to counter-intuitive phenomena. In this paper we shortly review noise
induced effects in different ecosystems, in which two populations compete for
the same resources. We also present new results on spatial patterns of two
populations, while modeling real distributions of anchovies and sardines. The
transient dynamics of these ecosystems are analyzed through generalized
Lotka-Volterra equations in the presence of multiplicative noise, which models
the interaction between the species and the environment. We find noise induced
phenomena such as quasi-deterministic oscillations, stochastic resonance, noise
delayed extinction, and noise induced pattern formation. In addition, our
theoretical results are validated with experimental findings. Specifically the
results, obtained by a coupled map lattice model, well reproduce the spatial
distributions of anchovies and sardines, observed in a marine ecosystem.
Moreover, the experimental dynamical behavior of two competing bacterial
populations in a meat product and the probability distribution at long times of
one of them are well reproduced by a stochastic microbial predictive model.Comment: 23 pages, 8 figures; to be published in Math. Model. Nat. Phenom.
(2016
Ecological Complex Systems
Main aim of this topical issue is to report recent advances in noisy
nonequilibrium processes useful to describe the dynamics of ecological systems
and to address the mechanisms of spatio-temporal pattern formation in ecology
both from the experimental and theoretical points of view. This is in order to
understand the dynamical behaviour of ecological complex systems through the
interplay between nonlinearity, noise, random and periodic environmental
interactions. Discovering the microscopic rules and the local interactions
which lead to the emergence of specific global patterns or global dynamical
behaviour and the noises role in the nonlinear dynamics is an important, key
aspect to understand and then to model ecological complex systems.Comment: 13 pages, Editorial of a topical issue on Ecological Complex System
to appear in EPJ B, Vol. 65 (2008
Stability and Hopf Bifurcation in a Delayed Predator-Prey System with Herd Behavior
A special predator-prey system is investigated in which the prey population exhibits herd behavior in order to provide a self-defense against predators, while the predator is intermediate and its population shows individualistic behavior. Considering the fact that there always exists a time delay in the conversion of the biomass of prey to that of predator in this system, we obtain a delayed predator-prey model with square root functional response and quadratic mortality. For this model, we mainly investigate the stability of positive equilibrium and the existence of Hopf bifurcation by choosing the time delay as a bifurcation parameter
Stochastic 0-dimensional Biogeochemical Flux Model: Effect of temperature fluctuations on the dynamics of the biogeochemical properties in a marine ecosystem
We present a new stochastic model, based on a 0-dimensional version of the well known biogeochemical flux model (BFM), which allows to take into account the temperature random fluctuations present in natural systems and therefore to describe more realistically the dynamics of real marine ecosystems. The study presents a detailed analysis of the effects of randomly varying temperature on the lower trophic levels of the food web and ocean biogeochemical processes. More in detail, the temperature is described as a stochastic process driven by an additive self-correlated Gaussian noise. Varying both correlation time and intensity of the noise source, the predominance of different plankton populations is observed, with regimes shifted towards the coexistence or the exclusion of some populations. Finally a Fourier analysis carried out on the time series of the plankton populations shows how the ecosystem responds to the seasonal driving for different values of the noise intensit
Spatiotemporal dynamics of a diffusive predator–prey model with fear effect
This paper concerned with a diffusive predator–prey model with fear effect. First, some basic dynamics of system is analyzed. Then based on stability analysis, we derive some conditions for stability and bifurcation of constant steady state. Furthermore, we derive some results on the existence and nonexistence of nonconstant steady states of this model by considering the effect of diffusion. Finally, we present some numerical simulations to verify our theoretical results. By mathematical and numerical analyses, we find that the fear can prevent the occurrence of limit cycle oscillation and increase the stability of the system, and the diffusion can also induce the chaos in the system
The buffered chemostat with non-monotonic response functions
We study how a particular spatial structure with a buffer impacts the number
of equilibria and their stability in the chemostat model. We show that the
occurrence of a buffer can allow a species to persist or on the opposite to go
extinct, depending on the characteristics of the buffer. For non-monotonic
response functions, we characterize the buffered configurations that make the
chemostat dynamics globally asymptotically stable, while this is not possible
with single, serial or parallel vessels of the same total volume and input
flow. These results are illustrated with the Haldane kinetic function.Comment: 9th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2013),
Toulouse : France (2013
Zombies: a simple discrete model of the apocalypse
A simple discrete-time two-dimensional dynamical system is constructed and analyzed numerically, with modelling motivations drawn from the zombie virus of popular horror fiction, and with suggestions for further exercises or extensions suitable for an introductory undergraduate course
Zombies: a simple discrete model of the apocalypse
A simple discrete-time two-dimensional dynamical system is constructed and analyzed numerically, with modelling motivations drawn from the zombie virus of popular horror fiction, and with suggestions for further exercises or extensions suitable for an introductory undergraduate course
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