Dilão R, Domingos T
Grupo de Dinâmica Não-Linear, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal.
Bull Math Biol. 2001 Mar;63(2):207-30. doi: 10.1006/bulm.2000.0213.
To describe the dynamics of a resource-dependent age structured population, a general non-linear Leslie type model is derived. The dependence on the resources is introduced through the death rates of the reproductive age classes. The conditions assumed in the derivation of the model are regularity and plausible limiting behaviors of the functions in the model. It is shown that the model dynamics restricted to its omega-limit sets is a diffeomorphism of a compact set, and the period-1 fixed points of the model are structurally stable. The loss of stability of the non-zero steady state occurs by a discrete Hopf bifurcation. Under general conditions, and after the loss of stability of the structurally stable steady states, the time evolution of population numbers is periodic or quasi-periodic. Numerical analysis with prototype functions has been performed, and the conditions leading to chaotic behavior in time are discussed.
为描述一个依赖资源的年龄结构种群的动态变化，推导了一个一般的非线性莱斯利型模型。通过生育年龄组的死亡率引入对资源的依赖性。模型推导过程中所假设的条件是模型中函数的正则性和合理的极限行为。结果表明，限制在其ω极限集上的模型动态是一个紧致集的微分同胚，并且模型的1周期不动点在结构上是稳定的。非零稳态的稳定性丧失是由离散霍普夫分岔引起的。在一般条件下，以及在结构稳定稳态的稳定性丧失之后，种群数量的时间演化是周期性的或准周期性的。已经使用原型函数进行了数值分析，并讨论了导致时间上混沌行为的条件。
