In this paper, the Adomian＇s decomposition method （ADM） is presented for finding the exact solutions of a more general biological population models. A new solution is constructed in power series. The fractional der...In this paper, the Adomian＇s decomposition method （ADM） is presented for finding the exact solutions of a more general biological population models. A new solution is constructed in power series. The fractional derivatives are described in the Caputo sense. To illustrate the reliability of the method, some examples are provided.展开更多
研究表明,现有的多目标进化算法在处理具有不同Pareto前沿的优化问题时难以有效平衡种群的收敛性与多样性.鉴于此,提出一种基于自适应参考向量和参考点的高维多目标进化算法(adaptive reference vector and reference point based many-...研究表明,现有的多目标进化算法在处理具有不同Pareto前沿的优化问题时难以有效平衡种群的收敛性与多样性.鉴于此,提出一种基于自适应参考向量和参考点的高维多目标进化算法(adaptive reference vector and reference point based many-objective evlolutionary algorithm, ARVRPMEA). ARVRPMEA主要利用种群稀疏性自适应调整参考向量和参考点以提高种群多样性,首先,生成均匀分布的参考向量子集和参考点子集,并利用该参考向量子集分解种群;然后,根据规模最大子种群中解的分布情况生成新的参考向量和参考点,直至满足参考向量集和参考点集规模;最后,为进一步提高种群收敛性,该算法结合指标进行环境选择以保存收敛性较高的个体进入下一代种群.实验结果表明, ARVRP算法在求解具有不同Pareto前沿的问题方面具有良好的性能.展开更多
In this paper, the dynamics of a stochastic model for algal bloom with nutrient recy- cling is investigated. The model incorporates a white noise term in the growth equation of algae population to describe the effects...In this paper, the dynamics of a stochastic model for algal bloom with nutrient recy- cling is investigated. The model incorporates a white noise term in the growth equation of algae population to describe the effects of random fluctuations in the environment, and a nutrient recycling term in the nutrient equation to account for the conversion of detritus into nutrient. The existence and uniqueness of the global positive solution of the model is first proved. Then we study the long-time behavior of the model. Conditions for the extinction and persistence in the mean of the algae population are established. By using the theory of integral Markov semigroups, we show that the model has an invari- ant and asymptotically stable density. Numerical simulations illustrate our theoretical results.展开更多
文摘In this paper, the Adomian＇s decomposition method （ADM） is presented for finding the exact solutions of a more general biological population models. A new solution is constructed in power series. The fractional derivatives are described in the Caputo sense. To illustrate the reliability of the method, some examples are provided.
文摘研究表明,现有的多目标进化算法在处理具有不同Pareto前沿的优化问题时难以有效平衡种群的收敛性与多样性.鉴于此,提出一种基于自适应参考向量和参考点的高维多目标进化算法(adaptive reference vector and reference point based many-objective evlolutionary algorithm, ARVRPMEA). ARVRPMEA主要利用种群稀疏性自适应调整参考向量和参考点以提高种群多样性,首先,生成均匀分布的参考向量子集和参考点子集,并利用该参考向量子集分解种群;然后,根据规模最大子种群中解的分布情况生成新的参考向量和参考点,直至满足参考向量集和参考点集规模;最后,为进一步提高种群收敛性,该算法结合指标进行环境选择以保存收敛性较高的个体进入下一代种群.实验结果表明, ARVRP算法在求解具有不同Pareto前沿的问题方面具有良好的性能.
基金This research is supported by the National Natural Science Foundation of China （11271260）, Innovation Program of Shanghai Municipal Education Committee （13ZZ116）, Shanghai Leading Academic Discipline Project （XTKX2012）, Hujiang Foundation of China （B14005） and China Scholarship Council.
文摘In this paper, the dynamics of a stochastic model for algal bloom with nutrient recy- cling is investigated. The model incorporates a white noise term in the growth equation of algae population to describe the effects of random fluctuations in the environment, and a nutrient recycling term in the nutrient equation to account for the conversion of detritus into nutrient. The existence and uniqueness of the global positive solution of the model is first proved. Then we study the long-time behavior of the model. Conditions for the extinction and persistence in the mean of the algae population are established. By using the theory of integral Markov semigroups, we show that the model has an invari- ant and asymptotically stable density. Numerical simulations illustrate our theoretical results.
