Pattern dynamics of vegetation based on optimal control theory

Vegetation pattern dynamics is a pivotal research domain in ecology, which can reveal the impact of the non-uniform distribution of vegetation on ecosystem structure and function. However, effectively managing and safeguarding these vegetation patterns to prevent ecological degradation remains challenging. The application of optimal control theory, a potent mathematical tool in ecology, has garnered significant attention. This review explores the application of optimal control theory in vegetation pattern dynamics, elucidating methods for achieving vegetation pattern phase transitions through control measures. Special emphasis is placed on the importance of optimal control in studying phase transitions of arid vegetation patterns, as well as the applicability of different control strategies for vegetation pattern management. Additionally, we envisage potential development directions of optimal control theory in future vegetation pattern dynamics research and discuss possible challenges and opportunities.