The noise-induced transition of the augmented Lotka-Volterra system is investigated under vanishingly small noise.Populations will ultimately go extinct because of intrinsic noise,and different extinction routes may o...The noise-induced transition of the augmented Lotka-Volterra system is investigated under vanishingly small noise.Populations will ultimately go extinct because of intrinsic noise,and different extinction routes may occur due to the Freidlin-Wentzell large deviation theory.The relation between the most probable extinction route(MPER)and heteroclinic bifurcation is studied in this paper.The MPERs and the quasi-potentials in different regimes of parameters are analyzed in detail.Before the bifurcation,the predator goes extinct,and the prey will survive for a long time.Then,the heteroclinic bifurcation changes the MPER wherein both species go extinct.The heteroclinic cycle plays a role in transferring the most probable extinction state.Moreover,the analyses of the weak noise limit can contribute to predicting the stochastic behavior under finite small noise.Both the heteroclinic bifurcation and the rotational deterministic vector field can reduce the action necessary for the MPER.展开更多
基金the National Natural Science Foundation of China(Grant Nos.11772149,and 12172167)A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education In-stitutions(PAPD)and The Research Fund of State Key Laboratory of Me-chanics and Control of Mechanical Structures(Grant No.MCMS-I-19G0l).
文摘The noise-induced transition of the augmented Lotka-Volterra system is investigated under vanishingly small noise.Populations will ultimately go extinct because of intrinsic noise,and different extinction routes may occur due to the Freidlin-Wentzell large deviation theory.The relation between the most probable extinction route(MPER)and heteroclinic bifurcation is studied in this paper.The MPERs and the quasi-potentials in different regimes of parameters are analyzed in detail.Before the bifurcation,the predator goes extinct,and the prey will survive for a long time.Then,the heteroclinic bifurcation changes the MPER wherein both species go extinct.The heteroclinic cycle plays a role in transferring the most probable extinction state.Moreover,the analyses of the weak noise limit can contribute to predicting the stochastic behavior under finite small noise.Both the heteroclinic bifurcation and the rotational deterministic vector field can reduce the action necessary for the MPER.
