Dynamical Complexity In Host-parasitoid Interaction Model

Chaos is a special characteristic of nonlinear dynamic system.Discrete-time host-parasitoid models have obvious nonlinearity and instability arose by interference and the dynamics can produce a much richer set of dynamic patterns than those observed in continuous-time models.The internal mechanisms of dynamical complexity are the important frontiers and hotspots in recent research.The subject of this dissertation focuses on this field:computer simulated research on dynamical complexity of population models.The dissertation will be separated into four parts:Chapter one and Chapter two summarize the creation and development of chaos theory,research methods,as well as the application in simply population models;Chapter three analyzes the dynamic complexities of host-parasitoid models with many kinds of functional responses;Chapter four focuses on the dynamic complexities of host-parasitoid model incorporating clumping effect; chapter five establishes a discrete-time host-parasitoid interaction model with Allee effct for the host and investigates the influence of Allee effect on the dynamic complexities. Finally,In the last chapter,I make the main conclusions and the perspectives about the development of chaos theory.Eight results and conclusions are obtained in this dissertation.1.The dynamic complexities of these host-parasitoid interaction models include Hopf bifurcation,Hopf bifurcation reversal,period-doubling bifurcation,period-halving, pitchfork bifurcation,pitchfork bifurcation reversal,attractor crises,chaotic bands with narrow or wide periodic windows,intermittent chaos,and supertransient behavior. Several types of attractors,e.g.two stable periodic,periodic vs.quasiperiodic and periodic vs.chaotic attractors,may coexist in the same mapping.This non-uniqueness also indicates that the bifurcation diagrams,or the routes to chaos, depend on initial conditions and are therefore non-unique.The basins of attraction, defining the initial conditions leading to a certain attractor,may be fractal set.The fractal property observed is the pattern of self-similarity.2.When parasitoid's attack to host random(without clumping effect),chaotic dynamics appear in large region of parameter.In the case of the parasitoid aggregation,the parameter region for persistent and stable interaction increases.So the parasitoid aggregation may be a strong stabilizing factor,which makes the stabile dynamic more strong. 3.Many authors have investigated clumping effect and all these research relied on field investigate and obtained some intriguing results that clumping effct can act as a stabilizing factor.Here,we simulate the behavior mechanism of parasite preying on host and the conclusions support the results obtained by field investigate.4.The intraspecifc interaction with Allee effect of host is favorable to the stabilization of the system,but it increases the risk of population becoming extinct and enlarges the range of parameters where population can not persist.5.The basins of attraction were defined as the set of the initial conditions whose trajectories asymptotically approach that attractor as time increases.The properties of self-similarity and fractal basin boundaries of the basins of attraction were found in many other models except host-parasitoid interaction model with Allee effct for the host.We obtained that Allee effct can eliminate the properties of self-similarity for the basins of attraction.6.Intermittent chaos and supertransients are not found in host-parasitoid interaction incorporating Allee effct model but we indeed find abrupt changes of steady period over the long time-scale.Even though all the control parameters are constant and no external noise is present,population size shifted suddenly from one stable period to another.It means Allee effct in host exclude the presence of chaos in the dynamics.7.The dynamic behavior of a population may dramatically be affcted by small changes in values of the parameters.Even if the parameter values and initial conditions remain unchanged,the trajectory may vary significantly as time passes.This shows that if the time series is too short,only a part of the dynamic structure may be detected.8.Though few examples of chaos were detected in wild populations,in the theoretical research the chaos phenomenon widely exists.The reason is that interspecifc interaction(parasitoid's attack to host aggregate)and intraspecifc interaction(Allee effct in host)avoids the trend that produces chaos.