Lie group classification of first-order delay ordinary differential equations

Abstract

A group classification of first-order delay ordinary differential equation (DODE) accompanied by an equation for delay parameter (delay relation) is presented. A subset of such systems (delay ordinary differential systems or DODSs) which consists of linear DODEs and solution independent delay relations have infinite-dimensional symmetry algebras, as do nonlinear ones that are linearizable by an invertible transformation of variables. Genuinely nonlinear DODSs have symmetry algebras of dimension $n$, $0\le n\le 3$. It is shown how exact analytical solutions of invariant DODSs can be obtained using symmetry reduction.

References in corpus (1)

• A mathematical model of granulopoiesis incorporating the negative feedback dynamics and kinetics of G-CSF/neutrophil binding and internalisation

Cited by in corpus (4)

• Linear or linearizable first-order delay ordinary differential equations and their Lie point symmetries
• Invariant compact finite difference schemes
• Lagrangian formalism and Noether-type theorems for second-order delay ODEs
• Conformally invariant elliptic Liouville equation and its symmetry preserving discretization