scholarly journals Stochastic sensitivity analysis of noise-induced intermittency and transition to chaos in one-dimensional discrete-time systems

2013 ◽  
Vol 392 (2) ◽  
pp. 295-306 ◽  
Author(s):  
Irina Bashkirtseva ◽  
Lev Ryashko
Keyword(s):  
Sensitivity Analysis ◽  
Discrete Time ◽  
One Dimensional ◽  
Transition To Chaos ◽  
Discrete Time Systems ◽  
Stochastic Sensitivity ◽  
Stochastic Sensitivity Analysis ◽  
Time Systems

Real-valued Deterministic Processes

2015 ◽  
Author(s):  
Arno Berger ◽  
Theodore P. Hill
Keyword(s):  
Differential Equations ◽  
Discrete Time ◽  
Random Systems ◽  
Benford’S Law ◽  
One Dimensional ◽  
Discrete Time Systems ◽  
Continuous Time Systems ◽  
Benford's Law ◽  
Deterministic Processes ◽  
Time Systems

In science, one-dimensional deterministic (i.e., non-random) systems provide the simplest models for processes that evolve over time. Mathematically, these models take the form of one-dimensional difference or differential equations. This chapter presents the basic theory of Benford's law for them. Specifically, it studies conditions under which these models conform to Benford's law by generating Benford sequences and functions, respectively. The first seven sections of the chapter focus on discrete-time systems (i.e., difference equations) because they are somewhat easier to work with explicitly. Once the Benford properties of discrete-time systems are understood, it is straightforward to establish the analogous properties for continuous-time systems (i.e., differential equations), which is done in the chapter's final section.

scholarly journals Preventing Noise-Induced Extinction in Discrete Population Models

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Irina Bashkirtseva
Keyword(s):  
Sensitivity Analysis ◽  
Population Models ◽  
Dimensional System ◽  
Mathematical Technique ◽  
One Dimensional ◽  
Stochastic Sensitivity ◽  
Ricker Model ◽  
Discrete Population ◽  
Discrete Population Models ◽  
Stochastic Sensitivity Analysis

A problem of the analysis and prevention of noise-induced extinction in nonlinear population models is considered. For the solution of this problem, we suggest a general approach based on the stochastic sensitivity analysis. To prevent the noise-induced extinction, we construct feedback regulators which provide a low stochastic sensitivity and keep the system close to the safe equilibrium regime. For the demonstration of this approach, we apply our mathematical technique to the conceptual but quite representative Ricker-type models. A variant of the Ricker model with delay is studied along with the classic widely used one-dimensional system.

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