The impacts of ocean plastic on the dynamics of marine populations

Abstract

In this research project, a generalized plastics-predator-prey model is introduced. The model can be used to study the impacts of plastics on two trophic levels of a food chain in marine ecosystems. The work presented here is restricted to one type of functional response, which is Holling IV functional response. The work is divided into two main chapters: Chapter 3 and Chapter 4. Chapter 3 considers the impact of constant plastics on the predator and prey populations. Chapter 4 examines the impact of time-varying plastics on the predator and prey populations. Chapter 3 investigates the short-term impacts caused by plastics through analytically and numerically studying the local stability and bifurcations in 1D caused by varying the constant level of plastics in the marine environment. Our theoretical derivations of bifurcations through proving Sotomayor’s Theorems for the system agreed with numerical simulations. The chapter also shows dynamic transitions occurred by bifurcations such as Hopf, transcritical and saddle-node. Chapter 4 investigates the long-term impacts caused by time-varying plastics. Hence, the influence of periodic plastics forcing on the system is scrutinized via numerical bifurcation analysis. Bifurcation diagrams are obtained by means of MATCONT that uses continuation technique. These diagrams contain a variety of codimension one bifurcation curves and codimension two bifurcation points. It is found that chaos through torus destruction takes place when the developed model is periodically-forced. Furthermore, the bifurcation diagrams give a wide range of complex dynamics such as multiple attractors, catastrophe and chaos through a cascade of period-doublings when the developed model’s three key baseline values are varied. Moreover, we find a larger number of multiple solutions of various periods in the unforced and forced dynamics, compared to other predator-prey systems with Holling IV functional response, especially when two of the three baseline values are changed.