Abstract
We shall explore a nonlinear discrete dynamical system that naturally occurs in population systems to describe a transmission of a trait from parents to their offspring. We consider a Mendelian inheritance for a single gene with three alleles and assume that to form a new generation, each gene has a possibility to mutate, that is, to change into a gene of the other kind. We investigate the derived models and observe chaotic behaviors of such models.
Highlights
Chaotic dynamical systems become very popular in science and engineering
There is no universal definition for chaos, the essential feature of chaos is sensitive dependence on initial conditions so that the eventual behavior of the dynamics is unpredictable
We are aiming to present some analytic results on dynamics of Vα : S2 → S2: Vα x12 x22 x32
Summary
Chaotic dynamical systems become very popular in science and engineering. Besides the original definition of the Li-Yorke chaos [1], there have been various definitions for “chaos” in the literature, and the most often used one is given by Devaney [2]. All examples of nonergodic QSO have been found in the class of Volterra QSO (see [10, 20, 21]) Based on these examples, the Ulam conjecture was modified as follows: any non Volterra QSO acting on the finite dimensional simplex is ergodic, that is, operators having chaotic behavior can be only found among Volterra QSO. The evolution of a mutation in population system having a single gene with two alleles always exhibits an ergodic behavior (or almost regular or almost stable). We consider an inheritance of a single gene with three alleles a1, a2, and a3 and show that a nonlinear dynamical system corresponding to the mutation exhibits a nonergodic and Li-Yorke chaotic behavior
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
