Related papers: Estimates for solutions in a predator-prey model d…
We study the chemostat model for one species competing for one nutrient using a Lyapunov-type analysis. We design the dilution rate function so that all solutions of the chemostat converge to a prescribed periodic solution. In terms of…
In this paper, we present new results on finite- and fixed-time convergence for dynamical systems using LaSalle-like invariance principles. In particular, we provide first and second-order non-smooth Lyapunov-like results for finite- and…
This paper concerns pattern formation in a class of reaction-advection-diffusion systems modeling the population dynamics of two predators and one prey. We consider the biological situation that both predators forage along the population…
The method of generalized modeling has been applied successfully in many different contexts, particularly in ecology and systems biology. It can be used to analyze the stability and bifurcations of steady-state solutions. Although many…
In this article, we develop a predator-prey model with Allee effect and prey group defense. The model has three equilibrium points i.e. the trivial point, the predator extinction point, and the coexistence point. All equilibrium points are…
In this paper, we investigate a discrete-time phytoplankton-zooplankton model that incorporates a linear predator functional response alongside a Holling-type toxin distribution. Both Holling type II and type III cases are considered, and…
A deterministic two-species predator-prey model with prey herd behavior is considered incorporating mutual interference and the effect of fear. We provide guidelines to the dynamical analysis of biologically feasible equilibrium points. We…
The stability analysis of a class of discontinuous discrete-time systems is studied in this paper. The system under study is modeled as a feedback interconnection of a linear system and a set-valued nonlinearity. An equivalent…
This paper concerns with the global dynamics of classical solutions to an important alarm-taxis ecosystem, which demonstrates the behaviors of prey that attract secondary predator when threatened by primary predator. And the secondary…
This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…
Ratio-dependent predator-prey models have been increasingly favored by field ecologists where predator-prey interactions have to be taken into account the process of predation search. In this paper we study the conditions of the existence…
We study species abundance in the empirical plant-pollinator mutualistic networks exhibiting broad degree distributions, with uniform intra-group competition assumed, by the Lotka-Volterra equation. The stability of a fixed point is found…
The paper is devoted to the study of stability of equilibrium solutions of a delay differential equation that models leukemia. The equation was previously studied in [5] and [6], where the emphasis is put on the numerical study of periodic…
We derive characteristic functions to determine the number and stability of relaxation oscillations for a class of planar systems. Applying our criterion, we give conditions under which the chemostat predator-prey system has a globally…
We study asymptotic behavior of solutions of the first-order linear consensus model with delay and anticipation, which is a system of neutral delay differential equations. We consider both the transmission-type and reaction-type delay that…
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…
In this paper, we consider the data-driven discovery of stable dynamical models with a single equilibrium. The proposed approach uses a basis-function parameterization of the differential equations and the associated Lyapunov function. This…
We consider an aggregation model for two interacting species. The coupling between the species is via their velocities, that incorporate self- and cross-interactions. Our main interest is categorizing the possible steady states of the…
Lyapunov stability of a mechanical system means that the dynamic response stays bounded in an arbitrarily small neighborhood of a static equilibrium configuration under small perturbations in positions and velocities. This type of stability…
We present new a stability result for periodic solutions of the periodic predator prey Lotka Volterra model, based on boundaries for the average of the coexistence states. Our result complements previous one in the literature.