System identification and landscape stability of stochastic competition ecosystem

Motivated by the challenging issue in analyzing the stochastic stability from observed state time series in a competition ecosystem, we take a systematic study from system identification to landscape stability. The vector field manifold is utilized to discuss dynamic properties of the deterministic competition ecosystem. For the stochastic state time series, we integrate the stochastic Koopman operator, the Kolmogorov backward equation and the extended dynamic mode decomposition methods to approximate the drift expression, while the Kramers-Moyal formula is used to identify the noise intensity. The depth and width indicators of the energy landscape are constructed to verify the effectiveness of the system identification method and to examine the impact of noise on system stability. Results demonstrate that proposed indicators can effectively assess the stochastic stability. Moreover, we find the environmental disturbance can induce global instability of the stochastic competition system, but its relative stability impact on each potential well will be altered by species competitiveness.