4,768 research outputs found
Stable scalable control of soliton propagation in broadband nonlinear optical waveguides
We develop a method for achieving scalable transmission stabilization and
switching of colliding soliton sequences in optical waveguides with
broadband delayed Raman response and narrowband nonlinear gain-loss. We show
that dynamics of soliton amplitudes in -sequence transmission is described
by a generalized -dimensional predator-prey model. Stability and bifurcation
analysis for the predator-prey model are used to obtain simple conditions on
the physical parameters for robust transmission stabilization as well as on-off
and off-on switching of out of soliton sequences. Numerical simulations
for single-waveguide transmission with a system of coupled nonlinear
Schr\"odinger equations with show excellent agreement with the
predator-prey model's predictions and stable propagation over significantly
larger distances compared with other broadband nonlinear single-waveguide
systems. Moreover, stable on-off and off-on switching of multiple soliton
sequences and stable multiple transmission switching events are demonstrated by
the simulations. We discuss the reasons for the robustness and scalability of
transmission stabilization and switching in waveguides with broadband delayed
Raman response and narrowband nonlinear gain-loss, and explain their advantages
compared with other broadband nonlinear waveguides.Comment: 37 pages, 7 figures, Eur. Phys. J. D (accepted
Revisiting the stability of spatially heterogeneous predator-prey systems under eutrophication
We employ partial integro-differential equations to model trophic interaction
in a spatially extended heterogeneous environment. Compared to classical
reaction-diffusion models, this framework allows us to more realistically
describe the situation where movement of individuals occurs on a faster time
scale than the demographic (population) time scale, and we cannot determine
population growth based on local density. However, most of the results reported
so far for such systems have only been verified numerically and for a
particular choice of model functions, which obviously casts doubts about these
findings. In this paper, we analyse a class of integro-differential
predator-prey models with a highly mobile predator in a heterogeneous
environment, and we reveal the main factors stabilizing such systems. In
particular, we explore an ecologically relevant case of interactions in a
highly eutrophic environment, where the prey carrying capacity can be formally
set to 'infinity'. We investigate two main scenarios: (i) the spatial gradient
of the growth rate is due to abiotic factors only, and (ii) the local growth
rate depends on the global density distribution across the environment (e.g.
due to non-local self-shading). For an arbitrary spatial gradient of the prey
growth rate, we analytically investigate the possibility of the predator-prey
equilibrium in such systems and we explore the conditions of stability of this
equilibrium. In particular, we demonstrate that for a Holling type I (linear)
functional response, the predator can stabilize the system at low prey density
even for an 'unlimited' carrying capacity. We conclude that the interplay
between spatial heterogeneity in the prey growth and fast displacement of the
predator across the habitat works as an efficient stabilizing mechanism.Comment: 2 figures; appendices available on request. To appear in the Bulletin
of Mathematical Biolog
Spectral control for ecological stability
A system made up of N interacting species is considered. Self-reaction terms
are assumed of the logistic type. Pairwise interactions take place among
species according to different modalities, thus yielding a complex asymmetric
disordered graph. A mathematical procedure is introduced and tested to
stabilise the ecosystem via an {\it ad hoc} rewiring of the underlying
couplings. The method implements minimal modifications to the spectrum of the
Jacobian matrix which sets the stability of the fixed point and traces these
changes back to species-species interactions. Resilience of the equilibrium
state appear to be favoured by predator-prey interactions
Community-driven dispersal in an individual-based predator-prey model
We present a spatial, individual-based predator-prey model in which dispersal
is dependent on the local community. We determine species suitability to the
biotic conditions of their local environment through a time and space varying
fitness measure. Dispersal of individuals to nearby communities occurs whenever
their fitness falls below a predefined tolerance threshold. The spatiotemporal
dynamics of the model is described in terms of this threshold. We compare this
dynamics with the one obtained through density-independent dispersal and find
marked differences. In the community-driven scenario, the spatial correlations
in the population density do not vary in a linear fashion as we increase the
tolerance threshold. Instead we find the system to cross different dynamical
regimes as the threshold is raised. Spatial patterns evolve from disordered, to
scale-free complex patterns, to finally becoming well-organized domains. This
model therefore predicts that natural populations, the dispersal strategies of
which are likely to be influenced by their local environment, might be subject
to complex spatiotemporal dynamics.Comment: 43 pages, 7 figures, vocabulary modifications, discussion expanded,
references added, Ecological Complexity accepte
Modeling population dynamics and economic growth as competing species: An application to CO2 global emissions
Since the beginning of the last century the world is experiencing an important demographic transition, which will probably impact on economic growth. Many demographers and social scientists are trying to understand the key drivers of such transition as well as its profound implications. A correct understanding will help to predict other important trends of the world primary energy demand and the carbon emission to the atmosphere, which may be leading to an important climate change. This paper proposes a set of coupled differential equations to describe the changes of population, gross domestic product, primary energy consumption and carbon emissions, modeled as competing-species as in Lokta-Volterra prey-predator relations. The predator–prey model is well known in the biological, ecological and environmental literature and has also been applied successfully in other fields. This model proposes a new and simple conceptual explanation of the interactions and feedbacks among the principal driving forces leading to the present transition. The estimated results for the temporal evolution of world population, gross domestic product, primary energy consumption and carbon emissions are calculated from year 1850 to year 2150. The calculated scenarios are in good agreement with common world data and projections for the next 100 years.Population dynamics, economic growth, primary energy consumption, carbon emission model, Lokta-Volterra Equations, Prey-predator model.
The conflict interaction between two complex systems. Cyclic migration
We construct and study a discrete time model describing the conflict
interaction between two complex systems with non-trivial internal structures.
The external conflict interaction is based on the model of alternative
interaction between a pair of non-annihilating opponents. The internal conflict
dynamics is similar to the one of a predator-prey model. We show that the
typical trajectory of the complex system converges to an asymptotic attractive
cycle. We propose an interpretation of our model in terms of migration
processes
Theoretical Study of Pest Control Using Stage Structured Natural Enemies with Maturation Delay: A Crop-Pest-Natural Enemy Model
In the natural world, there are many insect species whose individual members
have a life history that takes them through two stages, immature and mature.
Moreover, the rates of survival, development, and reproduction almost always
depend on age, size, or development stage. Keeping this in mind, in this paper,
a three species crop-pest-natural enemy food chain model with two stages for
natural enemies is investigated. Using characteristic equations, a set of
sufficient conditions for local asymptotic stability of all the feasible
equilibria is obtained. Moreover, using approach as in (Beretta and Kuang,
2002), the possibility of the existence of a Hopf bifurcation for the interior
equilibrium with respect to maturation delay is explored, which shows that the
maturation delay plays an important role in the dynamical behavior of three
species system. Also obtain some threshold values of maturation delay for the
stability-switching of the particular system. In succession, using the normal
form theory and center manifold argument, we derive the explicit formulas which
determine the stability and direction of bifurcating periodic solutions.
Finally, a numerical simulation for supporting the theoretical analysis is
given.Comment: 28 pages, 9 figure
Spatiotemporal dynamics in a spatial plankton system
In this paper, we investigate the complex dynamics of a spatial plankton-fish
system with Holling type III functional responses. We have carried out the
analytical study for both one and two dimensional system in details and found
out a condition for diffusive instability of a locally stable equilibrium.
Furthermore, we present a theoretical analysis of processes of pattern
formation that involves organism distribution and their interaction of
spatially distributed population with local diffusion. The results of numerical
simulations reveal that, on increasing the value of the fish predation rates,
the sequences spots spot-stripe mixtures
stripes hole-stripe mixtures holes wave pattern is
observed. Our study shows that the spatially extended model system has not only
more complex dynamic patterns in the space, but also has spiral waves.Comment: Published Pape
- …