赤潮藻类非线性动力学模型的随机分岔

Stochastic Bifurcation on HAB Nonlinear Stochastic Dynamics Model

选取典型赤潮藻类的硅藻和甲藻,建立了一个随机非线性动力学模型,运用随机平均法结合现代非线性动力学理论对模型进行了化简,运用拟不可积Hamilton系统的相关理论和Oseledec乘性遍历定理求解了模型的最大Lyapunov指数,得到了模型随机稳定性的条件;利用动态系统不变测度的Lyapunov指数分析了模型的随机分岔,得到了系统发生随机D-分岔时参数的取值条件,结果表明,系统在随机因素作用下变得更敏感、更不稳定。

A nonlinear stochastic dynamics model on HAB algae diatom and dianoflagellate densities was created and presented in this paper. By using a stochastic averaging method and modem nonlinear dynamical theory, the model was simplified. The max Lyapunov exponent was calculated through quasi non-integrable Hamiltonian system theory and Oseledec mutiplicative ergodic theory, the condition of the model＇s stochastic stability was obtained; the stochastic bifurcation was discussed by using the Lyapunov exponent of dynamical system invariant measure, and the parameter condition of stochastic D-bifurcation was also discussed in this paper. The result was that the stochastic system was more sensitive and unstable.