Chaos in Discrete Structured Population Models
نویسندگان
چکیده
We prove analytically the existence of chaotic dynamics in some classical discrete-time age-structured population models. Our approach allows us to estimate the sensitive dependence on the initial conditions, regions of initial data with chaotic behavior, and explicit ranges of parameters for which the considered models display chaos. These properties have important implications for evaluating the influence of a chaotic regime on the predictions based on mathematical models. We illustrate through particular examples how to apply our results.
منابع مشابه
A Note on the Convergence of the Homotopy Analysis Method for Nonlinear Age-Structured Population Models
In this paper, a theorem is proved which presents the series solution obtained from the homotopy analysis method is convergent to the exact solution of nonlinear age-structured population models.
متن کاملSome discrete-time SI, SIR, and SIS epidemic models.
Discrete-time models, or difference equations, of some well-known SI, SIR, and SIS epidemic models are considered. The discrete-time SI and SIR models give rise to systems of nonlinear difference equations that are similar in behavior to their continuous analogues under the natural restriction that solutions to the discrete-time models be positive. It is important that the entire system be cons...
متن کاملDynamics of Stage-structured Population Models with Harvesting Pulses
In most models of population dynamics, changes in population due to birth or harvesting are assumed to be time-independent, but many species reproduce or are caught only during a single period of the year. In this paper a single species stage-structured model with density-dependent maturation rate, birth pulse and harvesting pulse is formulated. Using the discrete dynamical system determined by...
متن کاملAttenuant cycles in periodically forced discrete-time age-structured population models
In discrete-time age-structured population models, a periodic environment is not always deleterious. We show that it is possible to have the average of the age class populations over an attracting cycle (in a periodic environment) not less than the average of the carrying capacities (in a corresponding constant environment). In our age-structured model, a periodic environment does not increase ...
متن کاملThe Time Invariance Principle, Ecological (Non)Chaos, andA Fundamental Pitfall of Discrete Modeling
This paper is to show that all but one discrete models used for population dynamics in ecology are inherently paradoxical that their predications cannot be independently verified by experiments because they violate a fundamental principle of physics. The result is used to resolve an on-going controversy regarding ecological chaos. Another implication of the result is that all continuous dynamic...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Applied Dynamical Systems
دوره 11 شماره
صفحات -
تاریخ انتشار 2012