Effect of seasonality on the dynamical behavior of an ecological system with impulsive control strategy

Yu, Hengguo; Zhong, Shouming; Agarwal, Ravi P.; Sen, Sagar

doi:10.1016/j.jfranklin.2011.01.009

Cited by 22 publications

(7 citation statements)

References 27 publications

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“…Seasonality is an important factor, which plays a vital role in describing the changes and fluctuations in ecological systems with predator-prey interactions [12][13][14][15][16][17][18]. Additionally, there are many ecological factors, such as hunting and climate, which have varied effects (positive and/or negative) on the dynamical behaviors of the species.…”

Section: Prefacementioning

confidence: 99%

Deterministic Sudden Changes and Stochastic Fluctuation Effects on Stability and Persistence Dynamics of Two-Predator One-Prey Model

Alebraheem

Elazab

Mohammed

et al. 2021

Journal of Mathematics

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In this paper, we present new results on deterministic sudden changes and stochastic fluctuations’ effects on the dynamics of a two-predator one-prey model. We purpose to study the dynamics of the model with some impacting factors as the problem statement. The methodology depends on investigating the seasonality and stochastic terms which make the predator-prey interactions more realistic. A theoretical analysis is introduced for studying the effects of sudden deterministic changes, using three different cases of sudden changes. We show that the system in a good situation presents persistence dynamics only as a stable dynamical behavior. However, the system in a bad situation leads to three main outcomes as follows: first, constancy at the initial conditions of the prey and predators; second, extinction of the whole system; third, extinction of both predators, resulting in the growth of the prey population until it reaches a peak carrying capacity. We perform numerical simulations to study effects of stochastic fluctuations, which show that noise strength leads to an increase in the oscillations in the dynamical behavior and became more complex and finally leads to extinction when the strength of the noise is high. The random noises transfer the dynamical behavior from the equilibrium case to the oscillation case, which describes some unstable environments.

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Section: Prefacementioning

confidence: 99%

Deterministic Sudden Changes and Stochastic Fluctuation Effects on Stability and Persistence Dynamics of Two-Predator One-Prey Model

Alebraheem

Elazab

Mohammed

et al. 2021

Journal of Mathematics

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“…In Figure 4, when prey and predator populations are plotted as a function of the probability , the value of is 1.45. In the former case, it is assumed that the foraging behavior of predator follows optimal foraging theory [16][17][18] and prey is more beneficial for predator than prey . In other words, the more beneficial prey is always included in the predator's diet, but if the density of prey falls below a critical threshold or goes to zero, prey is included with probability one.…”

Section: The Impulsive Effect and Optimal Foragingmentioning

confidence: 99%

“…In recent years, interest in studying nonlinear dynamic systems has exploded. In the 1970s, since the pioneering work of May on the relationship between food-web complexity and stability and the chaotic phenomenon [1][2][3], more and more researchers have become interested in dynamic behavior involving ecological mechanisms that promote species diversity [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. More recently, dynamic systems' studies have benefited from an infusion of interest and new techniques in ecology.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamic in an Ecological System with Impulsive Effect and Optimal Foraging

Zhao

Dai

2014

Abstract and Applied Analysis

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The population dynamics of a three-species ecological system with impulsive effect are investigated. Using the theories of impulsive equations and small-amplitude perturbation scales, the conditions for the system to be permanent when the number of predators released is less than some critical value can be obtained. Furthermore, because the predator in the system follows the predictions of optimal foraging theory, it follows that optimal foraging promotes species coexistence. In particular, the less beneficial prey can support the predator alone when the more beneficial prey goes extinct. Moreover, the influences of the impulsive effect and optimal foraging on inherent oscillations are studied using simulation, which reveals rich dynamic behaviors such as period-halving bifurcations, a chaotic band, a periodic window, and chaotic crises. In addition, the largest Lyapunov exponent and the power spectra of the strange attractor, which can help analyze the chaotic dynamic behavior of the model, are investigated. This information will be useful for studying the dynamic complexity of ecosystems.

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“…Consequently, it is natural to assume that these perturbations act instantaneously in the form of impulses. Thus impulsive differential equations and differential equations involving impulsive effects appear as a natural mathematical description (model) of observed evolution phenomena of several real world problems [17][18][19][20][21]. These works have introduced the theory of impulsive differential equations and its applications and provided a theoretical basis of the application of impulsive differential equations.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Mathematics and Sustainability in an Impulsive Eutrophication Controlling System

Zhao

Wang

2013

Abstract and Applied Analysis

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Eutrophication removal problems have captured the attention of biologists, mathematicians, and environmental scientists. Within this framework, an impulsive eutrophication controlling system is studied analytically and numerically. A key advantage of the eutrophication system is that it can be quite accurate to describe the interaction effect of some critical factors (fishermen catch and releasing small fry, etc.), which enables a systematic and logical procedure for fitting eutrophication mathematical system to real monitoring data and experiment data. Mathematical theoretical works have been pursuing the investigation of two threshold functions of some critical parameters under the condition of all species persistence, which can in turn provide a theoretical basis for the numerical simulation. Using numerical simulation works, we mainly focus on how to choose the best value of some critical parameters to ensure the sustainability of the eutrophication system so that the eutrophication removal process can be well developed with maximizing economic benefit. These results may be further extended to provide a basis for simulating the algal bloom in the laboratory and understanding the application of some impulsive controlling models about eutrophication removal problems.

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Effect of seasonality on the dynamical behavior of an ecological system with impulsive control strategy

Cited by 22 publications

References 27 publications

Deterministic Sudden Changes and Stochastic Fluctuation Effects on Stability and Persistence Dynamics of Two-Predator One-Prey Model

Deterministic Sudden Changes and Stochastic Fluctuation Effects on Stability and Persistence Dynamics of Two-Predator One-Prey Model

Nonlinear Dynamic in an Ecological System with Impulsive Effect and Optimal Foraging

Analysis of Mathematics and Sustainability in an Impulsive Eutrophication Controlling System

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