NDLI: MATCONT:a Matlab package for numerical bifurcation analysis of ODEs

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MATCONT:a Matlab package for numerical bifurcation analysis of ODEs

Content Provider	ACM Digital Library
Author	Dhooge, A. Govaerts, W. Kuznetsov, Yu. A.
Abstract	We consider generic parameterized autonomous ODEs of the form dx/dt ≡ ẋ = f(x, α), where x ∈ $ℝ^{n}$ is the vector of state variables, α ∈ $ℝ^{m}$ represents parameters, and f(x, α) ∈ $ℝ^{n}.$ There are several interactive software packages for analysis of dynamical systems defined by ODEs. The most widely used are AUTO86/97[1], CONTENT[2] and XPPAUT.The Matlab software package MATCONT provides an interactive environment for the continuation and normal form analysis of dynamical systems. This analysis is complementary to the simulation of the systems which is also included in the package and can be used in their identification, control, and optimization. MATCONT is designed to exploit the power of Matlab. It is developed in parallel with the continuation toolbox CL_MATCONT, a package of Matlab routines that can be used from the command line.We consider the following model of an autonomous electronic circuit where x, y and z are state variables and $β,γ,ν,r,a_{3},b_{3}$ are parameters: [see pdf for formula]We compute a branch of equilibria with free parameter ν stating from the trivial solution x = 0.00125, y = -0.001, z = 0.00052502 at β = 0.5, γ = -0.6, r = -0.6, $a_{3}$ = 0.32858, $b_{3}$ = 0.93358, ν = -0.9, ε = 0.001. We start a curve of periodic orbits from a Hopf point on this curve choosing ν as the free parameter. We detect a torus bifurcation point at ν = -0.59575. We continue the torus bifurcation in two parameters ν, ε and find that it shrinks to a single point for decreasing values of ν (Figure 2).
Starting Page	21
Ending Page	22
Page Count	2
File Format	PDF
ISSN	01635824
DOI	10.1145/980175.980184
Journal	ACM SIGSAM Bulletin (SIGS)
Volume Number	38
Issue Number	1
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1998-12-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article

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