Related papers: Finite time Blow up in a population model with com…
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…
In this paper, we develop a method of analyzing long transient dynamics in a class of predator-prey models with two species of predators competing explicitly for their common prey, where the prey evolves on a faster timescale than the…
Decarbonizing the global energy supply requires more efficient heating and cooling systems. Model predictive control enhances the operation of cooling and heating systems but depends on accurate system models, often based on control…
We prove the existence of traveling fronts in diffusive Rosenzweig-MacArthur and Holling-Tanner population models and investigate their relation with fronts in a scalar Fisher-KPP equation. More precisely, we prove the existence of fronts…
In this paper, we prove the existence and uniqueness of the global solution to the reaction diffusion system SKT with homogeneous Newmann boundary conditions. We use the lower and upper solution method and its associated monotone iterations…
This paper is devoted to the study of initial-boundary value problems for time-fractional analogues of Korteweg-de Vries, Benjamin-Bona-Mahony, Burgers, Rosenau, Camassa-Holm, Degasperis-Procesi, Ostrovsky and time-fractional modified…
Identifying early warning signs of sudden population changes and mechanisms leading to regime shifts are highly desirable in population biology. In this paper, a two-trophic ecosystem comprising of two species of predators, competing for…
Time-delay chaotic systems refer to the hyperchaotic systems with multiple positive Lyapunov exponents. It is characterized by more complex dynamics and a wider range of applications as compared to those non-time-delay chaotic systems. In a…
We present a rigorous framework for the local analysis of canards and slow passages through bifurcations in a wide class of infinite-dimensional dynamical systems with time-scale separation. The framework is applicable to models where an…
We derive an alternative expression for a delayed logistic equation in which the rate of change in the population involves a growth rate that depends on the population density during an earlier time period. In our formulation, the delay in…
We consider systems where a cycle born via the Hopf bifurcation blows up to infinity as a parameter ranges over a finite interval. Two examples demonstrating this effect are presented: planar Lotka-Volterra type systems with a…
We consider the model of economic growth with time delayed investment function. Assuming the investment is time distributed we can use the linear chain trick technique to transform delay differential equation system to equivalent system of…
In this paper, we consider a general single population model with delay and patch structure, which could model the population loss during the dispersal. It is shown that the model admits a unique positive equilibrium when the dispersal rate…
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…
Differential diffusion is a source of instability in population dynamics systems when species diffuse with different rates. Predator-prey systems show this instability only under certain specific conditions, usually requiring Holling-type…
Consider a nonlinear wave equation for a massless scalar field with self-interaction in the spatially flat de Sitter spacetime. We show that blow-up in a finite time occurs for the equation with arbitrary power nonlinearity as well as upper…
In this paper, robust finite-time consensus of a group of nonlinear multi-agent systems in the presence of communication time delays is considered. In particular, appropriate delay-dependent strategies which are less conservative are…
Living many-body systems often exhibit scale-free collective behavior reminiscent of thermal critical phenomena. But their mutual interactions are inevitably retarded due to information processing and delayed actuation. We numerically…
This paper addresses a press control problem in straightening machines with small time delays due to system communication. To handle this, we propose a generalized $\beta$-control method, which replaces conventional linear velocity control…
Logistic functions are good models of biological population growth. They are also popular in marketing in modelling demand-supply curves and in a different context, to chart the sales of new products over time. Delays being inherent in any…