Related papers: A Lotka-Volterra type model analyzed through diffe…
The global stability of the nonhomogeneous positive steady state solution to a diffusive Holling-Tanner predator-prey model in a heterogeneous environment is proved by using a newly constructed Lyapunov function and estimates of nonconstant…
In this paper, we investigate the well-posedness of weak solutions to the time-fractional Fokker-Planck equation. Its dynamics is governed by anomalous diffusion, and we consider the most general case of space-time dependent forces.…
Urban ecosystems exhibit complex predator-prey dynamics increasingly disrupted by anthropogenic disturbances (e.g., noise, habitat fragmentation). Classical Lotka-Volterra (LV) models fail to capture these human-induced stressors, and…
To describe population dynamics, it is crucial to take into account jointly evolution mechanisms and spatial motion. However, the models which include these both aspects, are not still well-understood. Can we extend the existing results on…
The linear instability of Lotka-Volterra orbits in the homogenous manifold of a two-patch system is analyzed. The origin of these orbits instability in the absence of prey migration is revealed to be the dependence of the angular velocity…
For a class of tempered fractional terminal value problems of the Caputo type, we study the existence and uniqueness of the solution, analyse the continuous dependence on the given data and using a shooting method, we present and discuss…
In this article, a non-smooth predator-prey dynamical system is considered. Here, we discuss about sustainable harvesting in a Filippov predator-prey system, which can produce yield and at the same time prevent over-exploitation of…
We extend Lyapunov--type Mittag--Leffler stability analysis for fuzzy nonlinear fractional differential equations (Caputo sense) and introduce a family of stronger, broadly applicable stability results. In particular, we develop (i) uniform…
In this paper, we consider the almost periodic dynamics of a multispecies Lotka-Volterra mutualism system with time varying delays on time scales. By establishing some dynamic inequalities on time scales, a permanence result for the model…
In the current study, we took into account a model of nonlinear ``predator-prey'' interactions including the ``Allee effect'' on both populations and disease in the predator population. The population as a whole is split into three: the…
Including spatial structure and stochastic noise invalidates the classical Lotka-Volterra picture of stable regular population cycles emerging in models for predator-prey interactions. Growth-limiting terms for the prey induce a continuous…
We study the probability of fixation in a stochastic two-species competition model. By identifying a naturally occurring fast timescale, we derive an approximation to the associated backward Kolmogorov equation that allows us to obtain an…
We investigate a two-state conformational conversion system and introduce a novel structure-preserving numerical scheme that couples a local discontinuous Galerkin space discretization with the backward Euler time-integration method. The…
All finite element methods, as well as much of the Hilbert-space theory for partial differential equations, rely on variational formulations, that is, problems of the type: find $u\in V$ such that $a(v,u) = l(v)$ for each $v\in L$, where…
We use dynamical generating functionals to study the stability and size of communities evolving in Lotka-Volterra systems with random interaction coefficients. The size of the eco-system is not set from the beginning. Instead, we start from…
We study the stability of linear fractional order maps. We show that in the stable region, the evolution is described by Mittag-Leffler functions and a well defined effective Lyapunov exponent can be obtained in these cases. For…
This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional…
We focus on the long term dynamics of "killing the winner" Lotka-Volterra models of marine communities consisting of bacteria, virus, and zooplankton. Under suitable conditions, it is shown that there is a unique equilibrium with all…
In this paper, a fractional derivative with short-term memory properties is defined, which can be viewed as an extension of Caputo fractional derivative. Then, some properties of the short memory fractional derivative are discussed. Also, a…
For years, a main focus of ecological research has been to better understand the complex dynamical interactions between species which comprise food webs. Using the connectance properties of a widely explored synthetic food web called the…