About this book
As a critical foundation of marine ecosystems, the frequent outbreaks of marine phytoplankton and the toxicity of planktonic animals pose significant threats to marine ecological security and human health. One of the primary reasons we currently struggle to effectively manage the safety issues surrounding marine plankton is the extremely complex nature of their growth environment, which exhibits intricate, dynamic and nonlinear characteristics.
To ultimately address this serious issue, this book begins with the nonlinear dynamic characteristics of marine plankton, focusing on the dynamic behaviour of both two-dimensional and spatiotemporal patterns. By constructing reaction-diffusion models and fractional diffusion systems of the planktonic ecosystem, the book characterises the various factors in different environments and studies the nonlinear behaviour of marine organisms. Employing linear stability theory, multi-scale analysis, comparison principle, analytical techniques, and the construction of Lyapunov functions, the book delves into the following topics: the stability of the plankton ecosystem, Hopf bifurcation, Turing bifurcation and other local bifurcations, spatial self-organisation behaviour of marine plankton, the formation of spatiotemporal patterns, and the persistence and extinction properties and characteristics. Marine ecology and the marine environment are currently hot research topics internationally, with the behaviour of marine organisms being a core area of this research.
The goal of exploring these issues is to scientifically understand the features of marine organisms, control their behaviour, manage ocean pollution effectively, contribute to human development, and support social advancement. Additionally, the authors aim to make academic contributions and provide guidance to graduate students and researchers dedicated to this field.
Contents
Preface
Chapter 1. Introduction
Chapter 2. Preliminaries
Chapter 3. The effect of stochastic marine environment
Chapter 4. The effect of marine environmental mutation
Chapter 5. The effect of time delay
Chapter 6. The effect of water temperature
Chapter 7. The effect of plankton cell size
Chapter 8. The effect of defensive and aggressive behavior
Chapter 9. The effect of schooling behavior and harvest
Chapter 10. The effect of toxin and cross-diffusion
Chapter 11. The effect of advection
Chapter 12. The effect of herd-taxis
Chapter 13. The effect of weakly nonlinear diffusion
Chapter 14. Temporal forcing induced pattern transitions
Chapter 15. Spatiotemporal dynamics near the Turing-Hopf bifurcation
Chapter 16. Fractional herd behavior with cross-diffusion
Chapter 17. Spatial fractional behavior with fear factor and refuge
Chapter 18. Spatial dynamics with time delay and Allee effect
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Biography
Prof. Shu Tang Liu received his PhD degree from South China University of Technology in 2002 (jointly trained by the City University of Hong Kong and South China University of Technology). He was awarded one of the One Hundred Excellent Doctoral Dissertations in 2004 in China (jointly organised and implemented by the Academic Degree Office of the State Council and the Ministry of Education, discipline of control theory and control engineering). He won the first prize for excellent scientific research achievements in Shandong colleges and universities. He is a member of the Center for Chaos and Complex Networks, a reviewer for American Mathematical Reviews, a member of the American Mathematical Society, and a member of the International WSEAS Automatic Committee. He serves as a reviewer for international journals such as Complex Systems, Transactions of the American Mathematical Society, IEEE Transactions on Circuits and Systems I: Regular Papers, Automatica, Fractals, Chaos, Solitons & Fractals, Nonlinear Analysis: Real World Applications, International Journal of Bifurcation and Chaos, Science China, Chinese Science Bulletin, and Acta Automatica Sinica. He has been engaged in scientific research in the fields of nonlinear system theory, fractal and chaos theory, nonlinear control and application, physical oceanography, marine environment, and marine ecology. He has published four monographs with Springer as the first author: Surface Chaos and Its Applications, Fractal Control Theory, Fractal Control and Its Applications, and Mathematical Principle and Fractal Analysis of Mesoscale Eddy and more than 200 papers in top journals and other journals both domestically and internationally.
Associate Prof. Li Zhang received her B.S. degree in mathematics and applied mathematics from the University of Jinan in 2003, an M.S. degree from Shandong University in 2006, and a PhD degree from Shandong University in 2011, China. Her current research interests include the control theory of chaos, fractals in social, financial and economic systems, and their applications. She, along with her co-authors, has published 9 journal papers in outlets such as SIAM Journal on Applied Dynamical Systems, Nonlinear Dynamics, Communications in Nonlinear Science and Numerical Simulation, Fractals, and International Journal of Bifurcation and Chaos, as well as 7 conference papers.
