发表机构
Bukhara State University; V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Science（布哈拉国立大学; 乌兹别克斯坦科学院 V.I.罗曼诺夫斯基数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文用同伦分析法求解连续时间两性群体Volterra二次随机算子，证明状态空间正不变性，给出ω-极限集条件、周期性与级数收敛性，并获显式解与高精度近似。
AI 中文摘要
本文利用同伦分析方法研究了一类两性群体Volterra二次随机算子的连续模拟的解析解。建立了系统状态空间的正不变性。通过Lyapunov函数，在系统系数的相应条件下，得到了ω-极限集的包含关系以及轨迹各分量的指数衰减估计。获得了离散模型与连续模型ω-极限集重合的充分条件。对于对角不变子集，建立了所有内部非平衡轨迹周期性的充分条件。通过优级数，在系统约化Jacobian的Hurwitz稳定性下，得到了同伦级数在[0,+∞)上绝对且一致收敛的充分条件。此外，对于遗传系数之间的特殊关系，找到了Cauchy问题的显式解析解。计算实验表明，同伦级数的项快速衰减，且仅使用展开的前几项就已具有良好的逼近精度。
英文摘要
This paper investigates analytical solutions of a continuous analogue of a class of Volterra quadratic stochastic operators of a two-sex population using the homotopy analysis method. The positive invariance of the state space of the system is established. By means of Lyapunov functions, inclusions for the $ω$-limit sets are obtained, together with exponential decay estimates for individual components of the trajectories under the corresponding conditions on the coefficients of the system. Sufficient conditions are obtained for the coincidence of the $ω$-limit sets of the discrete and continuous models. For the diagonal invariant subset, sufficient conditions are established for the periodicity of all interior non-equilibrium trajectories. By means of a majorant series, a sufficient condition for the absolute and uniform convergence of the homotopy series on $[0,+\infty)$ is obtained under the Hurwitz stability of the reduced Jacobian of the system. In addition, explicit analytical solutions of the Cauchy problem are found for special relations between the heredity coefficients. Computational experiments show a rapid decay of the terms of the homotopy series and good approximation accuracy already when using the first few terms of the expansion.
Comments39 pages, 4 figures
