132 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
A Holling-Tanner predator-prey model with strong Allee effect
We analyse a modified Holling-Tanner predator-prey model where the predation
functional response is of Holling type II and we incorporate a strong Allee
effect associated with the prey species production. The analysis complements
results of previous articles by Saez and Gonzalez-Olivares (SIAM J. Appl. Math.
59 1867-1878, 1999) and Arancibia-Ibarra and Gonzalez-Olivares (Proc. CMMSE
2015 130-141, 2015)discussing Holling-Tanner models which incorporate a weak
Allee effect. The extended model exhibits rich dynamics and we prove the
existence of separatrices in the phase plane separating basins of attraction
related to co-existence and extinction of the species. We also show the
existence of a homoclinic curve that degenerates to form a limit cycle and
discuss numerous potential bifurcations such as saddle-node, Hopf, and
Bogadonov-Takens bifurcations
Non-algebraic oscillations for predator-prey models
We prove that the limit cycle oscillations of the celebrated Rosenzweig-MacArthur differential system and other predator-prey models are non-algebraic
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
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
Analysis and simulation on dynamics of a partial differential system with nonlinear functional responses
We introduce a reaction–diffusion system with modified nonlinear functional responses. We first discuss the large-time behavior of positive solutions for the system. And then, for the corresponding steady-state system, we are concerned with the priori estimate, the existence of the nonconstant positive solutions as well as the bifurcations emitting from the positive constant equilibrium solution. Finally, we present some numerical examples to test the theoretical and computational analysis results. Meanwhile, we depict the trajectory graphs and spatiotemporal patterns to simulate the dynamics for the system. The numerical computations and simulated graphs imply that the available food resource for consumer is very likely not single
Dynamics Analysis of Modified Leslie-Gower Model with Simplified Holling Type IV Functional Response
In this paper, the modified Leslie-Gower predator-prey model with simplified Holling type IV functional response is discussed. It is assumed that the prey population is a dangerous population. The equilibrium point of the model and the stability of the coexistence equilibrium point are analyzed. The simulation results show that both prey and predator populations will not become extinct as time increases. When the prey population density increases, there is a decrease in the predatory population density because the dangerous prey population has a better ability to defend itself from predators when the number is large enough.Dalam tulisan ini dibahas modifikasi model mangsa pemangsa Leslie-Gower dan fungsi respon Holling tipe IV yang disederhanakan. Diasumsikan bahwa populasi mangsa adalah populasi yang berbahaya. Titik-titik kesetimbangan model dan kestabilan dari titik kesetimbangan koeksistensi dianalisis. Selanjutnya, dilakukan simulasi numerik pada titik kesetimbangan koeksistensi. Hasil simulasi menunjukkan bahwa kedua populasi mangsa dan pemangsa tidak akan punah pada saat waktu semakin membesar. Pada saat kepadatan populasi mangsa meningkat terjadi penurunan terhadap kepadatan populasi pemangsa karena populasi mangsa yang berbahaya memiliki kemampuan yang lebih baik untuk mempertahankan diri dari pemangsa ketika jumlahnya cukup besar
Optimal harvesting policy of a prey–predator model with Crowley–Martin-type functional response and stage structure in the predator
In this paper, a three-dimensional dynamical model consisting of a prey, a mature predator, and an immature predator is proposed and analysed. The interaction between prey and mature predator is assumed to be of the Crowley–Martin type, and both the prey and mature predator are harvested according to catch-per-unit-effort (CPUE) hypothesis. Steady state of the system is obtained, stability analysis (local and global both) are discussed to explore the long-time behaviour of the system. The optimal harvesting policy is also discussed with the help of Pontryagin's maximum principle. The harvesting effort is taken as an effective control instrument to preserve prey and predator and to maintain them at an optimal level
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