scholarly journals Lyapunov exponents and Oseledets decomposition in random dynamical systems generated by systems of delay differential equations

2020 ◽  
Vol 19 (4) ◽  
pp. 2235-2255
Author(s):  
Janusz Mierczyński ◽  
◽  
Sylvia Novo ◽  
Rafael Obaya ◽  
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Lyapunov Exponents ◽  
Delay Differential Equations ◽  
Random Dynamical Systems ◽  
Delay Differential

THREE TYPES OF SIMPLE DDE'S DESCRIBING TUMOR GROWTH

2007 ◽  
Vol 15 (04) ◽  
pp. 453-471 ◽  
Author(s):  
MAREK BODNAR ◽  
URSZULA FORYŚ
Keyword(s):  
Experimental Data ◽  
Dynamical Systems ◽  
Differential Equations ◽  
Tumor Growth ◽  
Delay Differential Equations ◽  
Ehrlich Ascites Tumor ◽  
Ascites Tumor ◽  
Ehrlich Ascites ◽  
Delay Differential

In this paper, we compare three types of dynamical systems used to describe tumor growth. These systems are defined as solutions to three delay differential equations: the logistic, the Gompertz and the Greenspan types. We present analysis of these systems and compare with experimental data for Ehrlich Ascites tumor in mice.

Search for Periodic Orbits in Delay Differential Equations

2014 ◽  
Vol 24 (06) ◽  
pp. 1450084 ◽  
Author(s):  
Romina Cobiaga ◽  
Walter Reartes
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Periodic Orbits ◽  
Heuristic Search ◽  
Delay Differential Equations ◽  
Anharmonic Oscillator ◽  
Analysis Method ◽  
Van Der Pol ◽  
Homotopy Analysis ◽  
Delay Differential

In a previous paper, we developed a new way to apply the Homotopy Analysis Method (HAM) in the search for periodic orbits in dynamical systems modeled by ordinary differential equations. This method differs from the original in the heuristic search of the frequencies of the cycles. In this paper, we show that the method can be extended to the search for periodic orbits in delay differential equations. Herein, this methodology is applied twice, firstly in an equation of van der Pol type and secondly in an anharmonic oscillator, both systems with a delayed feedback.

NUMERICAL INVESTIGATION OF D-BIFURCATIONS FOR A STOCHASTIC DELAY LOGISTIC EQUATION

2005 ◽  
Vol 05 (02) ◽  
pp. 211-222 ◽  
Author(s):  
NEVILLE J. FORD ◽  
STEWART J. NORTON
Keyword(s):  
Differential Equations ◽  
Lyapunov Exponents ◽  
Delay Differential Equations ◽  
Probability Distributions ◽  
Dynamical Behaviour ◽  
Stochastic Delay Differential Equations ◽  
Stochastic Delay ◽  
Delay Differential ◽  
Delay Logistic Equation ◽  
Parameter Dependent

This paper explores the use of numerical (approximation) methods in the detection of changes in the dynamical behaviour of solutions to parameter-dependent stochastic delay differential equations. We focus on the use of approximations to Lyapunov exponents. Using three numerical methods we begin to describe the probability distributions of the local approximate Lyapunov exponents and we use this information to enable us to predict values of the parameters at which solutions bifurcate. We conclude the paper by reviewing some of the potential pitfalls of using numerical simulations to detect the dynamical behaviour of the solutions to stochastic delay differential equations.

Sign in / Sign up

Export Citation Format

Share Document