Existence, uniqueness and exponential stability for stochastic fuzzy age-structured population equations with diffusion and Poisson jumps
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摘要: 把模糊和随机两种不确定性因素考虑到种群系统中, 得到一类具有年龄结构带 Poisson 跳的模糊随机种群扩散模型, 这类方程可用于混合动态系统的建模. 在方程系数满足有界条件(弱于线性增长条件) 和 Lipschitz 条件下, 运用逐次逼近法, 通过构造 Picard 迭代序列, 讨论了具有年龄结构带 Poisson 跳的模糊随机种群扩散方程解的存在性和唯一性. 利用 Gronwall 引理、模糊随机 $It\hat{\mathrm{o}}$ 积分的性质和三角不等式, 给出了方程强解存在的充分条件和近似解误差的估计式.Abstract: Considering the fuzziness and randomness, which are two kinds of uncertain factors in the population system, it is obtained that a class of stochastic fuzzy age-structured population equations with diffusion and Poisson jumps. Such equations can be useful in modeling of hybrid dynamic systems. Under the coefficients of the equation satisfying Lipschitz condition together with boundedness condition(which is weaker than linear growth condition), it can apply the method of successive approximation by constructing Picard iteration sequence to discuss the existence and uniqueness of solutions to stochastic fuzzy age-structured population equations with diffusion and Poisson jumps. Using Gronwall lemma、 fuzzy stochastic $It\hat{\mathrm{o}}$ integral and triangle inequality, the sufficient condition for the existence of the strong solution is given and an estimation of error of approximate solution is established.
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