Paper Info
Title
Symbolic analysis of bifurcations in planar variable structure systems
Abstract
In this paper a methodology to the analysis of bifurcations of variable structure systems is proposed. This methodology, based on the use of symbolic computation packages, is derived from the conditions of the existence of variable struc- ture bifurcations of planar systems, allowing a multi-parametric analysis, without intensive numeric computations. The proposal is applied to a predator-prey model with human intervention. I. INTRODUCTION Variable Structure Systems (VSS) have been widely studied over the years (1), (7), (9). This kind of systems could arise due discontinuities of the system, or due the application of discontinuous control laws. The study of the bifurcation of VSS, continues to receive attention, once: these bifurcations could lead to a complex behavior; the classification of these bifurcations is recent (5), (3); new procedures should be proposed to the computation of these bifurcations. The objective of this work is to show that methodologies based on symbolic computational procedures, could be applied to the bifurcation analysis of VSS. The major advantage of this proposal is that multi-parametric analysis could be carried out, overcoming intensive numerical computation. The conditions derived in this work could be implemented by using symbolic packages, following the theoretical statements. The proposed methodology relies on a nomenclature and a classification of bifurcations presented previously in (3). The conditions of existence of the bifurcations are presented for the planar case, but could be extended to higher dimen- sions. It is important to note that, the classification of the bifurcations presented in this work do not encompass all kinds of bifurcations of planar VSS, some kinds of global bifurcations such as limit-cycles bifurcations are not covered, for a comprehensive analysis see (8). However, following the same approach, these bifurcations could also be classified. Along the work, the features of the nomenclature and the classification are addressed. The application of the methodology is carried out for a predator-prey model with human exploitation. The analysis of this model allows a comparison with previuos works, where the bifurcation analysis is performed with numerical methods (5).
Year
DOI
Venue
2006
10.1109/ISCAS.2006.1693045
ISCAS
Keywords
Field
DocType
bifurcation,multivariable systems,predator-prey systems,symbol manipulation,variable structure systems,multiparametric analysis,planar systems,planar variable structure systems,predator-prey model,symbolic computation package,variable structure bifurcations
Control theory,Computer science,Symbolic computation,Planar,Symbolic data analysis,Multiparametric Analysis,Control system,Computation,Sliding mode control,Bifurcation
Conference
ISSN
Citations 
PageRank 
0271-4302
0
0.34
References 
Authors
1
3
Name
Order
Citations
PageRank
U. F. Moreno1204.23
E. B. Castelan2102.29
E. R. De Pieri381.07