Evolutionary tendency of vegetation systems at critical points - based on optimal control methods

Area of Science:

• Ecology
• Mathematical Biology
• Systems Ecology

Background:

• Arid vegetation systems exhibit complex spatial patterns and bifurcations influenced by parameters like precipitation.
• Understanding the dynamics at critical points in these systems is limited, despite extensive bifurcation theory research.
• Existing aridity classifications lack dynamical and mechanism-based interpretations of transitions between regimes.

Purpose of the Study:

• To systematically explore the evolutionary tendencies of arid vegetation systems at four representative critical points.
• To incorporate optimal control theory and human activities as a control variable in vegetation-water interaction models.
• To provide a novel theoretical framework for understanding critical point dynamics in arid ecosystems.

Main Methods:

• Incorporated optimal control theory into a vegetation-water interaction model, treating human activities as a control variable.
• Introduced four control tendency indicators (D_KL, PSNR, Cost, MRDR) to quantify transition difficulty from critical points to target steady states.
• Computed indicators along control trajectories to quantitatively compare and reveal system evolutionary tendencies at critical points.

Main Results:

• At Turing pattern critical points (p_T1, p_T2), vegetation systems evolve towards pattern states: p_T1 favors spot patterns, p_T2 favors gap patterns.
• At the desertification critical point (p_des), the system tends towards a bare soil state.
• At the transcritical bifurcation point (p_c), the system tends towards a uniform vegetation state.

Conclusions:

• This study is the first to characterize critical point evolutionary directions using optimal control, offering a new analytical tool for arid ecosystems.
• The findings refine aridity classification frameworks by incorporating critical points and their dynamics, providing a mechanism-based interpretation of regime transitions.
• The research highlights distinct evolutionary preferences at different critical points, crucial for understanding arid ecosystem stability and management.