Nonlinear dynamic analysis and numerical continuation of periodic orbits in high-index differential–algebraic equation systems

In this paper, we present a novel methodology for nonlinear dynamic analysis of chemical processes that are posed as differential–algebraic equations (DAE) systems. With the proposed approach, for the first time, high-index systems, which are often the result of computer-aided modeling, can be treat...

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Bibliographic Details
Published in:Nonlinear dynamics 2022-04, Vol.108 (2), p.1495-1507
Main Authors: Andrade Neto, Ataíde S., Secchi, Argimiro R., Melo, Príamo A.
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Approximation
Automotive Engineering
Chemical engineering
Chemical reactions
Classical Mechanics
Control
Differential equations
Dynamical Systems
Engineering
Hopf bifurcation
Mathematical models
Mechanical Engineering
Nonlinear dynamics
Orbits
Ordinary differential equations
Original Paper
Preconditioning
Reduction
Software
Stability analysis
Vibration
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Summary:In this paper, we present a novel methodology for nonlinear dynamic analysis of chemical processes that are posed as differential–algebraic equations (DAE) systems. With the proposed approach, for the first time, high-index systems, which are often the result of computer-aided modeling, can be treated “as is,” i.e. , without the need for model reformulation in order to fit in particular structures (such as the Hessenberg forms) or a preconditioning procedure such as index reduction. This is a desirable feature because special forms cannot always be achieved, and reduced-index systems may present a different behavior than the original one due to the well-known drift-off effect or even result in misleading stability conclusions. The main problems addressed here are the direct computation of Hopf bifurcation points and the stability analysis and numerical continuation of steady-state and periodic solutions. The developed algorithms were packed together in ContiNum, a MATLAB toolbox with free distribution. In order to illustrate the methodology, an example of a high-index system is discussed in detail, including the analysis of its low-index counterpart, showing that bifurcation diagrams can be accurately built without index reduction.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-022-07254-4