CHAOTIC HIERARCHY IN HIGH DIMENSIONS

2000 ◽  
Vol 14 (24) ◽  
pp. 2511-2527 ◽  
Author(s):  
D. E. POSTNOV ◽  
A. G. BALANOV ◽  
O. V. SOSNOVTSEVA ◽  
E. MOSEKILDE
Keyword(s):  
Discrete Time ◽  
Chaotic Behavior ◽  
Higher Order ◽  
Chaotic Attractors ◽  
Lyapunov Dimension ◽  
High Dimensions ◽  
Time Model ◽  
Discrete Time Model ◽  
The Creation

The paper suggests a new mechanism for the development of higher-order chaos in accordance with the concept of a chaotic hierarchy. A discrete-time model is proposed which demonstrates how the creation of coexisting chaotic attractors combined with boundary crises can produce a continued growth of the Lyapunov dimension of the resulting chaotic behavior.

Fractional-Order Calculus in Antimicrobial Resistance and Waning Vaccination

2020 ◽  
pp. 1-20
Author(s):  
E. Ahmed ◽  
Ahmed Ezzat Mohamed Matouk
Keyword(s):  
Antimicrobial Resistance ◽  
Fractional Order ◽  
Discrete Time ◽  
Local Stability ◽  
Chaotic Attractors ◽  
Time Model ◽  
Fractional Order Calculus ◽  
Discrete Time Model ◽  
Dynamical Behaviors ◽  
Numerical Tools

In this chapter, a simple model for competition between drug resistant and drug sensitive bacteria is given. So, a model of antimicrobial resistance (AMR) and waning vaccination is presented. The model's steady states are obtained. The conditions of local stability of the equilibria are also derived via the fractional Routh-Hurwitz criterion. A discretization scheme has also been applied to the proposed fractional-order model to enhance the model's adequacy and accuracy of describing natural phenomena. So, dynamical behaviors of the resulting discrete-time model are studied such as local stability, existence of Neimark-Sacker, and flip bifurcations. Furthermore, existence of chaos in the discrete-time model is proved using the theorem given by Marotto. Chaotic attractors and routes to chaos are also depicted via various numerical tools.

Non-homogeneous infinitely many sites discrete-time model with exact coalescent

2009 ◽  
Vol 33 (6) ◽  
pp. 713-732
Author(s):  
Adam Bobrowski ◽  
Marek Kimmel ◽  
Małgorzata Kubalińska
Keyword(s):  
Discrete Time ◽  
Time Model ◽  
Discrete Time Model
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