scholarly journals Small random perturbations of dynamical systems and the definition of attractors

1981 ◽  
Vol 82 (1) ◽  
pp. 137-151 ◽  
Author(s):  
David Ruelle
Keyword(s):  
Dynamical Systems ◽  
Random Perturbations ◽  
Small Random Perturbations ◽  
Definition Of

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.

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