11,072 research outputs found
Dynamics of a FitzHugh-Nagumo system subjected to autocorrelated noise
We analyze the dynamics of the FitzHugh-Nagumo (FHN) model in the presence of
colored noise and a periodic signal. Two cases are considered: (i) the dynamics
of the membrane potential is affected by the noise, (ii) the slow dynamics of
the recovery variable is subject to noise. We investigate the role of the
colored noise on the neuron dynamics by the mean response time (MRT) of the
neuron. We find meaningful modifications of the resonant activation (RA) and
noise enhanced stability (NES) phenomena due to the correlation time of the
noise. For strongly correlated noise we observe suppression of NES effect and
persistence of RA phenomenon, with an efficiency enhancement of the neuronal
response. Finally we show that the self-correlation of the colored noise causes
a reduction of the effective noise intensity, which appears as a rescaling of
the fluctuations affecting the FHN system.Comment: 13 pages, 10 figure
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
Asymptotic regime in N random interacting species
The asymptotic regime of a complex ecosystem with \emph{N}random interacting
species and in the presence of an external multiplicative noise is analyzed. We
find the role of the external noise on the long time probability distribution
of the i-th density species, the extinction of species and the local field
acting on the i-th population. We analyze in detail the transient dynamics of
this field and the cavity field, which is the field acting on the
species when this is absent. We find that the presence or the absence of some
population give different asymptotic distributions of these fields.Comment: 11 pages, 6 figures. To be published in Eur. Phys. J.
Transient behavior of a population dynamical model
The transient behavior of an ecosystem with N random interacting species in
the presence of a multiplicative noise is analyzed. The multiplicative noise
mimics the interaction with the environment. We investigate different
asymptotic dynamical regimes and the role of the external noise on the
probability distribution of the local field.Comment: 5 pages, 2 figures, accepted for publication in Progress of
Theoretical Physic
Role of the Colored Noise in Spatio-Temporal Behavior of Two Competing Species
We study the spatial distributions of two randomly interacting species, in
the presence of an external multiplicative colored noise. The dynamics of the
ecosystem is described by a coupled map lattice model. We find a nonmonotonic
behavior in the formation of large scale spatial correlations as a function of
the multiplicative colored noise intensity. This behavior is shifted towards
higher values of the noise intensity for increasing correlation time of the
noise.Comment: 6 pages, 3 figure
Nonmonotonic Pattern Formation in Three Species Lotka-Volterra System with Colored Noise
A coupled map lattice of generalized Lotka-Volterra equations in the presence
of colored multiplicative noise is used to analyze the spatiotemporal evolution
of three interacting species: one predator and two preys symmetrically
competing each other. The correlation of the species concentration over the
grid as a function of time and of the noise intensity is investigated. The
presence of noise induces pattern formation, whose dimensions show a
nonmonotonic behavior as a function of the noise intensity. The colored noise
induces a greater dimension of the patterns with respect to the white noise
case and a shift of the maximum of its area towards higher values of the noise
intensity.Comment: 6 pages, 3 figure
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