scholarly journals Random Dynamical Systems Generated by Two Allee Maps

2017 ◽  
Vol 27 (08) ◽  
pp. 1750117
Author(s):  
Jozef Kováč ◽  
Katarína Janková
Keyword(s):  
Dynamical Systems ◽  
Initial Conditions ◽  
Random Dynamical Systems ◽  
Deterministic System ◽  
Random Perturbations ◽  
Small Random Perturbations

In this paper, we study random dynamical systems generated by two Allee maps. Two models are considered — with and without small random perturbations. It is shown that the behavior of the systems is very similar to the behavior of the deterministic system if we use strictly increasing Allee maps. However, in the case of unimodal Allee maps, the behavior can dramatically change irrespective of the initial conditions.

scholarly journals Chaos and stability in some random dynamical systems

2012 ◽  
Vol 51 (1) ◽  
pp. 75-82
Author(s):  
Katarína Janková
Keyword(s):  
Dynamical Systems ◽  
Discrete Dynamical Systems ◽  
Random Dynamical Systems ◽  
Random Perturbations ◽  
Continuous Maps ◽  
Small Random Perturbations

ABSTRACT Nonchaotic behavior in the sense of Li and Yorke chaos in discrete dynamical systems generated by a continuous selfmapping of a real compact inter- val means that every trajectory can be approximated by a periodic one. Stability of this behavior was analyzed also for dynamical systems with small random perturbations. In this paper we study similar properties for nonautonomous periodic dynamical systems with random perturbations and for random dynamical systems generated by two continuous maps and their perturbations.

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