With the rapid development of science and technology, the loss of biodiversity and the degradation of ecosystems are becoming increasingly important for human survival and development. This article adopts the theory of dynamic transition to investigate the spatial dynamics characteristics of the Lotka-Volterra competitive model with diffusion terms. It determines the new solution expressions for the system transitioning from zero to nonzero solutions and utilizes spectral theory of linear fully continuous fields to demonstrate continuous transitions occurring when the bifurcation parameter exceeds the stability threshold of the system. Finally, the theoretical findings are validated using finite difference method. The research results obtained in this paper have certain theoretical significance and application value, which can be applied in many practical aspects, providing a strong theoretical basis for the protection of ecological stability and diversity.

Naiqiao Zhao, Ni Cheng, Yifan Jiang. Predictive studies of the Lotka-Volterra biocompetitive system based on transition theory. Academic Journal of Mathematical Sciences (2024) Vol. 5, Issue 1: 70-80. https://doi.org/10.25236/AJMS.2024.050111.

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