Year-end Sale % OFF 
Abstract
Using piecewise constant orthonormal functions, an approximation of the monodromy operator of a Linear Periodic Delay Differential Equation (PDDE) is obtained by approximating the integral equation corresponding to the PDDE as a linear operator over the space of initial conditions. This approximation allows us to consider the state space as finite dimensional resulting in a finite matrix approximation whose spectrum converges to the spectrum of the monodromy operator.
Highlights
Linear Periodic Differential Equations (PDDEs) have been of importance for studying problems of vibration, mechanics, astronomy, electric circuits, biology among others in [1] several examples of delay effects on mechanical systems are given, in [2] and [3] effects of the delay in physics and biological processes are considered
Using piecewise constant orthonormal functions, an approximation of the monodromy operator of a Linear Periodic Delay Differential Equation (PDDE) is obtained by approximating the integral equation corresponding to the PDDE as a linear operator over the space of initial conditions
Convergence of k and its spectrum is stated in Theorems 10, 14 and 15. This approximation is made by projecting the integral equation corresponding to the PDDE in to a a finite dimensional subspace spanned by finitely many piecewise constant functions
Summary
Linear Periodic Differential Equations (PDDEs) have been of importance for studying problems of vibration, mechanics, astronomy, electric circuits, biology among others in [1] several examples of delay effects on mechanical systems are given, in [2] and [3] effects of the delay in physics and biological processes are considered. The main contribution is an approximation of the monodromy operator of the PDDE by a linear Equation (35) of the form x = k x0 , where the directly obtained matrix k will correspond to the approximated monodromy operator, with no need of approximating solutions or numerical integration. Convergence of k and its spectrum is stated in Theorems 10, 14 and 15 This approximation is made by projecting the integral equation corresponding to the PDDE in to a a finite dimensional subspace spanned by finitely many piecewise constant functions. The main goal of this paper is to provide a computationally light method, with straightforward implementation, to approximate the monodromy operator of a delay differential equation, in order to facilitate the computation of stability diagrams used to study the behavior of the equation with respect to changes in its parameters
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
