| 摘要 | 第8-10页 |
| Abstract | 第10-11页 |
| Chapter 1 Introduction | 第12-25页 |
| 1.1 Background | 第12-17页 |
| 1.2 Preliminaries | 第17-25页 |
| 1.2.1 Stochastic integration with Brown motion | 第17-19页 |
| 1.2.2 Stochastic integration with L(?)vy jumps | 第19-20页 |
| 1.2.3 Free boundary problem | 第20-21页 |
| 1.2.4 Stochastic integration with Multi-fractional Brown motion | 第21-22页 |
| 1.2.5 Some useful inequalities | 第22-25页 |
| Chapter 2 Analysis of a Matualism Model with Stchastic Perturbations | 第25-42页 |
| 2.1 Model and preliminary resluts | 第25-28页 |
| 2.2 Existence and uniqueness of the positive solution | 第28-30页 |
| 2.3 Stochastically ultimate boundedness, Uniformly Holder-continuous and Stochastic permanence | 第30-35页 |
| 2.4 Persistence in mean and extinction | 第35-40页 |
| 2.5 Numerical simulations | 第40-42页 |
| Chapter 3 Analysis of a non-autonomous mutualism model driven by L(?)vy jumps | 第42-57页 |
| 3.1 Models and resluts | 第42-44页 |
| 3.2 Existence and uniqueness of the positive solution | 第44-46页 |
| 3.3 Stochastically ultimate boundedness and Stochastic permanence | 第46-49页 |
| 3.4 Persistence in mean and extinction | 第49-57页 |
| Chapter 4 Existence of global solution to a mutualistic model with double fronts | 第57-90页 |
| 4.1 Introduction and resluts | 第57-59页 |
| 4.2 Existence and uniqueness | 第59-65页 |
| 4.3 Global bounded solution | 第65-69页 |
| 4.4 Global fast solution and grow up solution | 第69-73页 |
| 4.5 Spreading-vanishing dichotomy | 第73-84页 |
| 4.6 Estimates of spreading speed | 第84-90页 |
| Chapter 5 Non-autonomous Gilpin-Ayala Equation Driven by Multifrac-tional noise | 第90-98页 |
| 5.1 Introduction for the Problem | 第90-92页 |
| 5.2 Preliminaries | 第92-93页 |
| 5.3 Well-posedness for Non-autonomous Gilpin-Ayala Equation Driven by Multifractional noise | 第93-98页 |
| Bibliography | 第98-107页 |
| Publications and Finished Papers | 第107-108页 |
| Acknowledgements | 第108页 |
