Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale

2016 ◽  
Vol 26 (7) ◽  
pp. 073104 ◽  
Author(s):  
Oleg V. Maslennikov ◽  
Vladimir I. Nekorkin
Keyword(s):  
Discrete Time ◽  
Time Scale ◽  
Chaotic Dynamics ◽  
Fast Time ◽  
Fast Time Scale ◽  
Discrete Time Systems ◽  
Time Systems

scholarly journals Local Observability of Systems on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Zbigniew Bartosiewicz
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Time Scale ◽  
Analytic Functions ◽  
Analytic Geometry ◽  
Discrete Time Systems ◽  
Continuous Time Systems ◽  
Real Analytic ◽  
Time Systems ◽  
Real Analytic Geometry

Analytic systems on an arbitrary time-scale are studied. As particular cases they include continuous-time and discrete-time systems. Several local observability properties are considered. They are characterized in a unified way using the language of real analytic geometry, ideals of germs of analytic functions, and their real radicals. It is shown that some properties related to observability are preserved under various discretizations of continuous-time systems.

scholarly journals Non-linear population discrete models with two time scales: re-scaling of part of the slow process

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Luis Sanz ◽  
Rafael Bravo de la Parra ◽  
Marcos Marvá ◽  
Eva Sánchez
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Linear Models ◽  
Discrete Models ◽  
Fast Time ◽  
Compact Sets ◽  
Practical Applications ◽  
Fast Time Scale ◽  
Non Linear ◽  
Time Systems

Abstract In this work we present a reduction result for discrete-time systems with two time scales. In order to be valid, previous results in the field require some strong hypotheses that are difficult to check in practical applications. Roughly speaking, the iterates of a map as well as their differentials must converge uniformly on compact sets. Here, we eliminate the hypothesis of uniform convergence of the differentials at no significant cost in the conclusions of the result. This new result is then used to extend to non-linear cases the reduction of some population discrete models involving processes acting at different time scales. In practical cases, some processes that occur at a fast time scale are often only measured at slow time intervals, notably mortality. For a general class of linear models that include such a kind of processes, it has been shown that a more realistic approach requires the re-scaling of those processes to be considered at the fast time scale. We develop the same type of re-scaling in some non-linear models and prove the corresponding reduction results. We also provide an application to a particular model of a structured population in a two-patch environment.

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