Related papers: Predator-prey models with memory and kicks: Exact …
We classify the global dynamics of a family of Kolmogorov systems depending on three parameters which has ecological meaning as it modelizes a predator-prey system. We obtain all their topologically distinct global phase portraits in the…
We develop a mathematical model of extinction and coexistence in a generic predator-prey ecosystem composed of two herbivores in asymmetrical competition and a hunter exerting a predatory pressure on both species. With the aim of…
Mathematical modeling based on time-delay differential equations is an important tool to study the role of delay in biological systems and to evaluate its impact on the asymptotic behavior of their dynamics. Delays are indeed found in many…
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.…
To understand the spreading and interaction of prey and predator, in this paper we study the dynamics of the diffusive Lotka-Volterra type prey-predator model with different free boundaries. These two free boundaries, which may intersect…
Long and short memory in economic processes is usually described by the so-called discrete fractional differencing and fractional integration. We prove that the discrete fractional differencing and integration are the Grunwald-Letnikov…
This paper deals with ratio-dependent predator-prey systems with delay. We will investigate under what conditions delay cannot cause instability in higher dimension. We give an example when delay causes instability.
Repeated games have provided an explanation how mutual cooperation can be achieved even if defection is more favorable in a one-shot game in prisoner's dilemma situation. Recently found zero-determinant strategies have substantially been…
A machine learning method is proposed using two agents that simulate the biological behavior of a predator and a prey. In this method, the predator and the prey interact with each other - the predator chases the prey while the prey runs…
We investigate the win-lose relations between strategies of iterated prisoner's dilemma games by using a directed network concept to display the replicator dynamics results. In the giant strongly-connected component of the win/lose network,…
Field equations with time and coordinates derivatives of noninteger order are derived from stationary action principle for the cases of power-law memory function and long-range interaction in systems. The method is applied to obtain a…
In this investigation we study the effects of climate change on predator-prey population dynamics. The interaction of predator and prey is described by the Variable Territory (VT) model with Allee effects in an Ordinary Differential…
1. Spatial memory plays a role in the way animals perceive their environments, resulting in memory-informed movement patterns that are observable to ecologists. Developing mathematical techniques to understand how animals use memory in…
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…
We prove the existence of infinitely many periodic solutions and complicated dynamics, due to the presence of a topological horseshoe, for the classical Volterra predator--prey model with a periodic harvesting. The proof relies on some…
Since the introduction of zero-determinant strategies, extortionate strategies have received considerable interest. While an interesting class of strategies, the definitions of extortionate strategies are algebraically rigid, apply only to…
Modeling a structured, dynamic environment like a video game requires keeping track of the objects and their states declarative knowledge) as well as predicting how objects behave (procedural knowledge). Black-box models with a monolithic…
Fractional differential equations model processes with memory effects, providing a realistic perspective on complex systems. We examine time-delayed differential equations, discussing first-order and fractional Caputo time-delayed…
We unify two different periodicity mechanisms: delayed self-regulation and planar predator-prey feedback. We consider scalar delay differential equations $\dot x(t) = rf(x(t), x(t - 1))$ where $f$ is monotone in the delayed component. Due…
Honest signals and cues have been observed as part of interspecific and intraspecific communication among animals. Recent theories suggest that existing signaling systems have evolved through natural selection imposed by predators. Honest…