本书运用反应扩散理论、稳定性理论、拓扑度理论等研究源于生物、化学反应中的反应扩散系统的相关动力学性质。具体内容包括：热力学中自催化反应扩散系统、带有非单调反应函数的捕食反应扩散生态系统、多种群周期反应扩散生态系统、带有毒素与联合非选择性收益的竞争反应扩散生态系统、具有年龄结构的多种群反应扩散生态系统、浮游植物-营养质反应扩散生态系统以及具有交叉扩散现象的广义捕食反应扩散生态系统共存态的有界性、稳定性、存在性、周期性、长时行为以及混沌行为等动力学性质。

Preface
Main Symbols
Chapter 1 Preliminaries-Basic Theory 1
1.1 Maximum Principle and Upper-Lower Solution Method of Partial Differential Equations of Second Order 1
1.2 Eigenvalue Problems and Variational Principle 4
1.3 Theory of Fixed Point Index and Topological Degree in Banach Spaces 5
1.4 Theory of Bifurcation and Stability in Banach Spaces 6
Chapter 2 Autocatalytic Reaction-Diffusion Chemical System in Thermodynamics 9
2.1 Introduction 9
2.2 Characteristic on Coexistent States 12
2.2.1 A Priori Estimate 12
2.2.2 Fundamental Properties 14
2.3 Stability of Constant Coexistent State 19
2.4 Non-Constant Coexistent States 22
2.4.1 Nonexistence 22
2.4.2 Existence 25
2.5 Existence and Uniqueness of Bifurcation Emanating from Constant Coexistence 29
2.5.1 Take the Concentration of Reaction Precursor as the Parameter 29
2.5.2 Take the Diffusion Rate of Reactant or Autocatalyst as the Parameter 36
2.6 Numerical Simulations 40
2.7 Notes 40
Chapter 3 Predator-Stage Structured Reaction-Diffusion Biosystem 43
3.1 The System 43
3.2 A Priori Estimate 46
3.3 Stability 48
3.4 Existence of Non-Constant Coexistent States 53
3.5 Analysis on Hopf Bifurcation 61
3.6 Notes 64
Chapter 4 Periodic Reaction-Diffusion Biosystems of Multi-Species 65
4.1 Competitive Type 65
4.1.1 Introduction 65
4.1.2 A Priori Estimate 67
4.1.3 Asymptotic Behavior 70
4.2 Cooperative Type 79
4.2.1 Introduction 79
4.2.2 A Priori Estimate and Existence of Coexistent States 81
4.2.3 Steady-State System 89
4.3 An Example-Two Species System with Nonlinear Functional Response 96
4.3.1 The System and Preliminaries 96
4.3.2 Existence， Uniqueness and Nonexistence of Coexistent States 97
4.3.3 Numerical Simulations 103
4.4 Notes 105
Chapter 5 Prey-Refuge Presented Reaction-Diffusion Biosystem 107
5.1 The System 107
5.2 Effects of Refuge on Stability 109
5.3 Existence of Predator and Prey with Refuge Consideration 110
5.4 Notes 126
Chapter 6 Reaction-Diffusion Competing Ecosystem with Harvesting and Toxicity 129
6.1 The System 129
6.2 Stability Analysis 130
6.3 Bifurcation Emanating from Double Eigenvalue 135
6.4 Multiplicity of Non-Constant Coexistent States 136
6.5 Coexistent States with Biologic and Economic Considerations 138
6.6 Numerical Simulations 140
6.7 Notes 141
Chapter 7 Reaction-Diffusion Marine Ecosystem of Phytoplankton-Nutrient 142
7.1 Introduction 142
7.2 Long-Time Behavior 144
7.3 Stability 147
7.4 A Priori Estimate 149
7.5 Patterns of Non-Constant Coexistent States 153
7.6 Notes 158
Chapter 8 Reaction-Diffusion Predator-Prey Population System with Fractional Response 159
8.1 The System 159
8.2 Global Attractor and Persistence 160
8.3 Stability of Constant Coexistent State 163
8.4 Bifurcation Emanating from Constant Coexistent State 164
8.5 Existence of Coexistent States 172
8.6 Notes 177
Chapter 9 Population Systems with Cross-Diffusion 178
9.1 Competitive Type 178
9.1.1 The System 178
9.1.2 Stability 180
9.1.3 Boundedness 181
9.1.4 Non-Existence and Existence of Coexistent States 183
9.2 Predator-Prey Type 188
9.2.1 The System 189
9.2.2 A Priori Estimate 191
9.2.3 Stability 193
9.2.4 Existence of Non-Constant Coexistent States 195
9.3 Notes 201
Chapter 10 Global Analysis for Reaction-Diffusion Biological and Biochemical Systems 202
10.1 Ecological System with Non-Selective Harvesting 202
10.1.1 The System 202
10.1.2 Local Bifurcation and Stability 205
10.1.3 Existence of Global Bifurcation 209
10.1.4 Notes 215
10.2 Biochemical Reaction System with Oncolytic Virus 216
10.2.1 Introduction 216
10.2.2 A priori Estimate and Stability 218
10.2.3 Global Bifurcation Analysis 220
10.2.4 Notes 228
Bibliography 229