Pattern Dynamics of Marine Plankton Behavior

Prof. Liu received his Ph. D. 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 organized 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 Cocmmittee. 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 in 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. Zhang received her B.S. degree in mathematics and applied mathematics from University of Jinan in 2003, an M.S. degree from Shandong University in 2006, and a Ph.D. degree from Shandong University in 2011, China. Her current research interests include the control theory of chaos, fractal 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.

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.