Research On Ecological Spatiotemporal Complexity Based On Coupled Map Lattices

Spatiotemporal complexity in ecosystem is a frontier and hot issue in contemporary ecology. It reveals a variety of spatiotemporal self-organizing structures in ecosystems. In the theoretical research of ecological spatiotemporal complexity, reaction diffusion models occupy the core position. Developed based on discretizing the reaction diffusion model, coupled map lattice model has important significances in further discovering formation mechanisms and transition regularities of the spatiotemporal self-organizing structures. In this thesis, we deconstruct and descretize the processes of reaction and spatial movement in the reaction diffusion models. A nonlinear alternatively iterative relationship is taken between the two processes to establish coupled map lattice models. Based on the coupled map lattice models, we carry out investigations on the spatiotemporal complexity of three types of reaction diffusion systems, including reaction self-diffusion system, reaction convection diffusion system and reaction self-and cross-diffusion system. Via stability analysis, bifurcation analysis, Turing instability analysis and numerical simulation and analysis on the reaction diffusion systems described by the coupled map lattices, the research reveals the self-organization of a variety of spatiotemporal ordered and disordered structures. The following results are stated:(1) In the reaction self-diffusion predator-prey system of Beddington-DeAngelis type, the spatiotemporal dynamics of the system can be separated into four regions, stable homogeneous stationary state region, Neimark-Sacker instability region, pure Turing instability region and Neimark-Sacker-Turing instability region; in the pure Turing instability region and Neimark-Sacker-Turing instability region, the system shows self-organizing formation of many types of patterns, such as patterns of spots, stripes, gaps, labyrinth, circles and spirals; the patterns forming under the mechanism of Neimark-Sacker-Turing instability may have the characteristics of spatiotemporal chaos.(2) In the reaction convection diffusion system based on the space-and time-discrete Klausmeier model, the system can reproduce the self-organizing formation of various types of vegetation patterns in semiarid regions via Turing instability mechanism, such as mosaic, spot, regular striped, fractured striped and arc vegetation patterns; change of rainfall can affect the characteristics of vegetation patterns, including patch area, patch density or width of vegetation stripes; change of plant diffusion capability can affect the degree of fragmentation of vegetation patterns, resulting to the transition betweem inmmigrating patterns and stationary patterns; the simulation results of vegetation patterns show agreement with field observation, successfully explaining the diversity and complexity of vegetation patterns self-organized in semiarid regions.(3) In the reaction self-and cross-diffusion predator-prey system, the system can show many spatially homogeneous bahaviors, such as homogeneous stationary state, homogeneous periodic oscillating state, homogeneous quasiperiodic oscillating state and homogeneous chaotic oscillating state; the pure Turing instability occurring on the homogeneous stationary state can lead to the formation of patterns of labyrinth, gaps, stripes, spots and mosaics; the Neimark-Sacker-Turing instability occurring on the homogeneous periodic/quasiperiodic oscillating state can result to the formation of patterns of arcs, spirals and circles; the Neimark-Sacker-Turing instability occurring on the homogeneous chaotic oscillating state can also lead to the self-organizing formation of spatiotemporal ordered structure, revealing the ordering regularity concealed behind chaos.(4) The research on the route to chaos and pattern formation in reaction diffusion system demonstrates that, flip bifurcation and Neimark-Sacker bifurcation can start the routes from stable homogeneous stationary state to the homogeneous chaotic oscillating state; that when flip-Turing instability mechanism takes place, the reaction diffusion system can show spatial period-doubling process on the route to chaos, leading to a transition from ordered pattern states to spatiotemporal disordered states; that when Neimark-Sacker-Turing instability occurs, the pattern formation and pattern transition of the reaction diffusion system on the route to chaos are not only driven by the Turing instability mechanism, but also influenced by the spatial movement of the state variables; that in the reaction convection diffusion system, the system may change from spatiotemporal disordered state to spatiotemporal ordered state, meaning that the spatiotemporal disordering process on the route to chaos can be reversed.In this thesis, we investigates the ecological spatiotemporal complexity based on coupled map lattices, exploring the pattern formation mechanisms of three types of space-and time-discrete reaction diffusion systems, discovering rich spatiotemporal self-organized structures, revealing the regularities of formation and transition of spatial patterns. The research provides theoretical basis for further understanding and predicting the spatiotemporal behaviors of ecological systems.