Abstract
This paper gives an analytical proof of the existence of chaotic dynamics for a single-species discrete population model with stage structure and birth pulses. The approach is based on a general existence criterion for chaotic dynamics of n-dimensional maps and inequality techniques. An example is given to illustrate the effectiveness of the result.
Highlights
Many papers have been published on chaos in discrete models
Since numerical simulations may lead to erroneous conclusions, numerical evidence of the existence of chaotic behaviors still needs to be confirmed analytically
Liz and Ruiz-Herrera [ ] established a general existence criterion for chaotic dynamics of n-dimensional maps under a new definition of chaos, and they applied it to prove analytically the existence of chaotic dynamics in some classical discrete-time age-structured population models. This novel analytical approach is very effective in detecting chaos of discrete-time dynamical systems
Summary
1 Introduction Many papers have been published on chaos in discrete models (see [ – ] and references cited therein). Some researchers proved analytically the existence of chaotic behavior of discrete systems under different definitions of chaos (for example, see [ – ]). Liz and Ruiz-Herrera [ ] established a general existence criterion for chaotic dynamics of n-dimensional maps under a new definition of chaos, and they applied it to prove analytically the existence of chaotic dynamics in some classical discrete-time age-structured population models.
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