Complex Dynamics in a Harvested Nutrient-Phytoplankton-Zooplankton Model with Seasonality

Abstract

A nutrient-phytoplankton-zooplankton model is established, where harvest effort on phytoplankton population and seasonal intrinsic growth of nutrient biomass are considered. Positivity and boundedness of solutions of model system are studied. By analyzing the characteristic equation of linearized system corresponding to the proposed model system, local asymptotic stability around interior equilibrium is studied, which reveals that interior equilibrium loses its stability at some critical value of predation rate. By utilizing Poincaré surface of section and computation of Lyapunov exponents, numerical experiments are performed to discuss the complex dynamical behavior of model system. Model system shows rich dynamic behavior including limit cycle and chaotic attractor due to variation of predation rate and seasonal intrinsic growth rate. Further numerical experiments show that reasonable harvesting has stabilizing effect on population dynamics that prevents chaotic behavior. Numerical simulations are carried out to show consistency with theoretical analysis obtained in this paper.

Dynamic Complexity of a Phytoplankton-Fish Model with the Impulsive Feedback Control by means of Poincaré Map

“…where u and v represent the population density of phytoplankton and fish at the moment, respectively, and E is the effort for continuous harvesting. For details of other parameters, see [34][35][36].…”

Dynamic Analysis of a Phytoplankton-Fish Model with the Impulsive Feedback Control Depending on the Fish Density and Its Changing Rate

“…Due to its importance in applications, in recent years, systems of impulsive differential equations have attracted more and more attention and been applied to different areas from population dynamics to chemical regulator systems [21][22][23][24][25][26][27][28]. Due to the challenges in analysing these models, most of existing models only considered the population size without considering the population growth rate when proposing a control strategy [29,30]. However it would be more reasonable if both growth rate and population size are taken into consideration when developing a capture strategy.…”