Related papers: Impact of Delay on Predator-Prey Models
We study the impact of competing time delays in coupled stochastic synchronization and coordination problems. We consider two types of delays: transmission delays between interacting elements and processing, cognitive, or execution delays…
Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard…
Delay-Differential Equations (DDEs) are the most common representation for systems with delay. However, the DDE representation is limited. In network models with delay, the delayed channels are low-dimensional and accounting for this…
Experiments in predator-prey systems show the emergence of long-term cycles. Deterministic model typically fails in capturing these behaviors, which emerge from the microscopic interplay of individual based dynamics and stochastic effects.…
This paper investigates the long-term dynamics of a reaction-diffusion predator-prey system subject to random environmental fluctuations modeled by Markovian switching. The model is formulated as a hybrid system of partial differential…
The primary goal of this research is to investigate the impact of delay on the dynamics of the Susceptible-Exposed-Infected-Recovered-Death and Susceptible (SEIRDS) model, to which we add a stochastic term to account for uncertainty in…
Stemming from the stochastic Lotka-Volterra or predator-prey equations, this work aims to model the spatial inhomogeneity by using stochastic partial differential equations (SPDEs). Compared to the classical models, the SPDE model is more…
The spiking properties of a subcritical Hopf oscillator with a time delayed nonlinear feedback is investigated. Finite time delay is found to significantly affect both the statistics and the fine structure of the spiking behavior. These…
Real-world systems can be strongly influenced by time delays occurring in self-coupling interactions, due to unavoidable finite signal propagation velocities. When the delays become significantly long, complicated high-dimensional phenomena…
Real-world processes often exhibit temporal separation between actions and reactions - a characteristic frequently ignored in many modelling frameworks. Adding temporal aspects, like time delays, introduces a higher complexity of problems…
In the wake of the 2020 COVID-19 epidemic, much work has been performed on the development of mathematical models for the simulation of the epidemic, and of disease models generally. Most works follow the susceptible-infected-removed (SIR)…
We consider a stochastic individual based model where each predator searches during a random time and then manipulates its prey or rests. The time distributions may be non-exponential. An age structure allows to describe these interactions…
We investigate the effect of turning delays on the behaviour of groups of differential wheeled robots and show that the group-level behaviour can be described by a transport equation with a suitably incorporated delay. The results of our…
Systems whose time evolutions are entirely deterministic can nevertheless be studied probabilistically, i.e. in terms of the evolution of probability distributions rather than individual trajectories. This approach is central to the…
Active agents with time-delayed interactions arise naturally in various real-world systems, such as biological systems, transportation networks and robotic swarms. Such systems are typically modeled as Delay Differential Equations (DDEs)…
The numerical convergence of a Telegraph Predator-Prey system is studied. This system of partial differential equations (PDEs) can describe various biological systems with reactive, diffusive and delay effects. Initially, our problem is…
Procrastination, the irrational delay of tasks, is a common occurrence in online learning. Potential negative consequences include higher risk of drop-outs, increased stress, and reduced mood. Due to the rise of learning management systems…
In this paper, we extend the demographic eco-evolutionary game approach, based on explicit birth and death dynamics instead of abstract "fitness" interpreted as an abstract "Malthusian parameter", by the introduction of the delay resulting…
Time delay in general leads to instability in some systems, while a specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a non-stationary stochastic…
We study a stochastic model of protein dynamics that explicitly includes delay in the degradation. We rigorously derive the master equation for the processes and solve it exactly. We show that the equations for the mean values obtained…