A stage-structured single species model with pulse input in a polluted environment

Abstract

In this paper, we study a stage-structured single species model with pulse input in a polluted environment. Using the discrete dynamical system determined by the stroboscopic map, we obtain the globally attractive condition for the species-extinction periodic solution of the investigated system. By the use of the theory of impulsive delayed differential equation, we also obtain sufficient condition of the permanence of the investigated system. Our results reveal that long mature period of the population in polluted environment can cause it to go extinct.

Persistence and Extinction of a Stochastic Single-Species Population Model in a Polluted Environment With Impulsive Toxicant Input

“…Owing to its theoretical and practical significance, population model in a polluted environment with pulse toxicant input has deserved a lot of attention (see e.g. [3,13,14,15,16,17,33,35,38,39]), but mainly in deterministic case. The present paper is the first attempt, up to our knowledge, of such a study in a stochastic setting.…”

“…From then on, many important deterministic models were proposed and studied, see e.g. [2,3,4,9,10,11], [13]- [18], [28,29,31], [33]- [39] and the references cited therein. Particularly, Liu, Chen and Zhang [16] proposed a single-species population model in a polluted environment with impulsive toxicant input.…”

The Role of Harvesting in Population Control in Presence of Multiple Stochastic Noise Sources

“…In a theoretical ecologist's point of view the question of bio-diversity of an ecological system is directly related to stability of the system. Results of stability analysis of various deterministic population models have been reported by many authors [1,2]. The study of models with noise are becoming increasingly important in various branches of science [3][4][5][6][7][8].…”

Stability and Permanence of a Pest Management Model with Impulsive Releasing and Harvesting

“…Therefore, how to effectively control insects and other arthropods has become an increasingly complex issue. Usually, chemical pesticides were taken as a relatively simple way to solve the pest-related problems, and some mathematical models on pest management with toxin (pesticide) input were studied in [1][2][3][4]. However, the overuse of chemical pesticides may create new ecological and sociological harm such as pesticide pollution and pesticideresistant pest varieties and inflicts harmful effects on humans and so forth.…”

“…Recently, some biocontrol models on pest management described by impulsive differential equation were proposed and the dynamics such as stability, permanence, periodicity, and bifurcation are deeply investigated (see also, e.g., [2][3][4][5][6][7][8][9][10][11][12]). In [5], an impulsive system to model the process of periodic releasing natural enemies and harvesting pest at different fixed time for pest control is considered, and the sufficient conditions on the existence and global stability of the periodic solution are derived for the given model.…”