scholarly journals Pseudospectral reduction to compute Lyapunov exponents of delay differential equations

2018 ◽  
Vol 23 (7) ◽  
pp. 2727-2741 ◽  
Author(s):  
Dimitri Breda ◽  
◽  
Sara Della Schiava
Keyword(s):  
Differential Equations ◽  
Lyapunov Exponents ◽  
Delay Differential Equations ◽  
Delay Differential

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.

A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3157-3172
Author(s):  
Mujahid Abbas ◽  
Bahru Leyew ◽  
Safeer Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Metric Space ◽  
Delay Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

Mass Transport Modelling in Porous Media Using Delay Differential Equations

2006 ◽  
Vol 258-260 ◽  
pp. 586-591
Author(s):  
António Martins ◽  
Paulo Laranjeira ◽  
Madalena Dias ◽  
José Lopes
Keyword(s):  
Porous Media ◽  
Differential Equations ◽  
Mass Transport ◽  
Delay Differential Equations ◽  
Dispersion Model ◽  
Flow Characteristics ◽  
Convective Transport ◽  
Transport Modelling ◽  
Flow Field Characteristics ◽  
Delay Differential

In this work the application of delay differential equations to the modelling of mass transport in porous media, where the convective transport of mass, is presented and discussed. The differences and advantages when compared with the Dispersion Model are highlighted. Using simplified models of the local structure of a porous media, in particular a network model made up by combining two different types of network elements, channels and chambers, the mass transport under transient conditions is described and related to the local geometrical characteristics. The delay differential equations system that describe the flow, arise from the combination of the mass balance equations for both the network elements, and after taking into account their flow characteristics. The solution is obtained using a time marching method, and the results show that the model is capable of describing the qualitative behaviour observed experimentally, allowing the analysis of the influence of the local geometrical and flow field characteristics on the mass transport.

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