Dual fear phenomenon in an eco-epidemiological model with prey aggregation

This study presents a thorough analysis of an eco-epidemiological model that integrates infectious diseases in prey, prey aggregation, and the dual fear effect induced by predators. We establish criteria for determining the existence of equilibrium points, which carry substantial biological significance. We establish the conditions for the occurrence of Hopf, saddle-node, and transcritical bifurcations by employing fear parameters as key bifurcation parameters. Furthermore, through numerical simulations, we demonstrate the occurrence of multiple zero-Hopf (ZH) and saddle-node transcritical (SNTC) bifurcations around the endemic steady states by varying specific key parameters across the two-parametric plane. We demonstrate that the introduction of predator-induced fear, which hinders the growth rate of susceptible prey, can lead to the finite time extinction of an initially stable susceptible prey population. Finally, we discuss management strategies aimed at regulating disease transmission, focusing on fear-based interventions and selective predation via predator attack rate on infectious prey

Dynamic analysis of a fractional-order single-species model with diffusion

In this paper, we consider a fractional-order single-species model which is composed of several patches connected by diffusion. We first prove the existence, uniqueness, non-negativity and boundedness of solutions for the model, as desired in any population dynamics. Moreover, we also obtain some sufficient conditions ensuring the existence and uniform asymptotic stability of the positive equilibrium point for the investigated system. Finally, numerical simulations are presented to demonstrate the validity and feasibility of the theoretical results

Persistence of nonautonomous logistic system with time-varying delays and impulsive perturbations

In this paper, we develop the impulsive control theory to nonautonomous logistic system with time-varying delays. Some sufficient conditions ensuring the persistence of nonautonomous logistic system with time-varying delays and impulsive perturbations are derived. It is shown that the persistence of the considered system is heavily dependent on the impulsive perturbations. The proposed method of this paper is completely new. Two examples and the simulations are given to illustrate the proposed method and results

On Agent Communication in Large Groups

The problem is fundamental and natural, yet deep - to simulate the simplest possible form of communication that can occur within a large multi-agent system. It would be prohibitive to try and survey all of the research on communication in general so we must restrict our focus. We will devote our efforts to synthetic communication occurring within large groups. In particular, we would like to discover a model for communication that will serve as an abstract model, a prototype, for simulating communication within large groups of biological organisms

Evolutionary games on graphs

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.Comment: Review, final version, 133 pages, 65 figure

Dynamic analysis of two fishery capture models with a variable search rate and fuzzy biological parameters

The fishery resource is a kind of important renewable resource and it is closely connected with people's production and life. However, fishery resources are not inexhaustible, so it has become an important research topic to develop fishery resources reasonably and ensure their sustainability. In the current study, considering the environment changes in the system, a fishery model with a variable predator search rate and fuzzy biological parameters was established first and then two modes of capture strategies were introduced to achieve fishery resource exploitation. For the fishery model in a continuous capture mode, the dynamic properties were analyzed and the results show that predator search rate, imprecision indexes and capture efforts have a certain impact on the existence and stability of the coexistence equilibrium. The bionomic equilibrium and optimal capture strategy were also discussed. For the fishery model in a state-dependent feedback capture mode, the complex dynamics including the existence and stability of the periodic solutions were investigated. Besides the theoretical results, numerical simulations were implemented step by step and the effects of predator search rate, fuzzy biological parameters and capture efforts on the system were demonstrated. This study not only enriched the related content of fishery dynamics, but also provided certain reference for the development and utilization of fishery resources under the environment with uncertain parameters

Dynamics of Bacterial white spot disease spreads in Litopenaeus Vannamei with time-varying delay

In this paper, we mainly consider a eco-epidemiological predator-prey system where delay is time-varying to study the transmission dynamics of Bacterial white spot disease in Litopenaeus Vannamei, which will contribute to the sustainable development of shrimp. First, the permanence and the positiveness of solutions are given. Then, the conditions for the local asymptotic stability of the equilibriums are established. Next, the global asymptotic stability for the system around the positive equilibrium is gained by applying the functional differential equation theory and constructing a proper Lyapunov function. Last, some numerical examples verify the validity and feasibility of previous theoretical results