Bifurcations in Piecewise-smooth Continuous Systems (World by David John Warwick Simpson

By David John Warwick Simpson

Real-world platforms that contain a few non-smooth switch are frequently well-modeled through piecewise-smooth platforms. in spite of the fact that there nonetheless stay many gaps within the mathematical concept of such structures. This doctoral thesis offers new effects relating to bifurcations of piecewise-smooth, non-stop, self sufficient structures of normal differential equations and maps. a variety of codimension-two, discontinuity brought on bifurcations are opened up in a rigorous demeanour. a number of of those unfoldings are utilized to a mathematical version of the expansion of Saccharomyces cerevisiae (a universal yeast). the character of resonance close to border-collision bifurcations is defined; specifically, the curious geometry of resonance tongues in piecewise-smooth non-stop maps is defined intimately. Neimark-Sacker-like border-collision bifurcations are either numerically and theoretically investigated. A entire history part is comfortably supplied for people with very little adventure in piecewise-smooth structures.

Show description

Read Online or Download Bifurcations in Piecewise-smooth Continuous Systems (World Scientific Series on Nonlinear Science Series a) PDF

Similar linear books

Banach Algebras (Modern Analytic and Computational Methods in Science and Mathematics)

Banach algebras are Banach areas outfitted with a continual binary operation of multiplication. various areas thought of in useful research also are algebras, e. g. the distance C(0, 1) with pointwise multiplication of features, or the distance l1 with convolution multiplication of sequences. Theorems of the final conception of Banach algebras, utilized to these areas, yield a number of classical result of research, e.

The Linear Algebra a Beginning Graduate Student Ought to Know, Second Edition

This booklet carefully offers with the summary thought and, while, devotes huge house to the numerical and computational facets of linear algebra. It includes a huge variety of thumbnail pics of researchers who've contributed to the improvement of linear algebra as we all know it this present day and likewise comprises over 1,000 workouts, a lot of that are very not easy.

Descriptive Topology and Functional Analysis: In Honour of Jerzy Kakol's 60th Birthday

Descriptive topology and practical research, with broad fabric demonstrating new connections among them, are the topic of the 1st component to this paintings. purposes to areas of constant services, topological Abelian teams, linear topological equivalence and to the separable quotient challenge are integrated and are offered as open difficulties.

Extra resources for Bifurcations in Piecewise-smooth Continuous Systems (World Scientific Series on Nonlinear Science Series a)

Example text

Determining the existence and admissibility of cycles of higher period in terms of the multipliers of AL and AR is a far more difficult task, see Chapter 6. For an extension of Feigin’s results to piecewise-smooth, discontinuous maps, see [Dutta et al. (2008)]. Under smooth parameter variation, periodic cycles may collide with a switching manifold. e. 11). This is shown in Chapter 6. Hence Feigin’s results may also be used to determine the admissibility of n and 2n-cycles local to this border-collision bifurcation [di Bernardo et al.

Then PL (c1 ) = eT 2 ϕT (0, c1 ; µ) where T is the L transition time obtained by solving eT 1 ϕT (0, c1 ; µ) = 0. Unfortunately this X last equation is transcendental (like e cos(X) = 2). Consequently qµ has no known explicit form. This exemplifies a recurring theme regarding discontinuous bifurcations: local dynamics may be determined by global properties of a piecewise-linear system. 21), are attracting and repelling foci for arbitrarily small values of µ. In this scenario, near the discontinuous bifurcation there exists a unique admissible equilibrium.

Now suppose there are no sliding regions in a neighborhood of the grazing point. When the grazing trajectory, Γ, is admissible, as in Fig. 8(a2), the grazing point is known as a regular grazing point. The criterion of November 26, 2009 15:34 World Scientific Book - 9in x 6in Fundamentals of Piecewise-Smooth, Continuous Systems bifurcations 29 no sliding generally corresponds to adding a codimension to the bifurcation, however in practice underlying physical assumptions often eliminate the possibility for sliding motion.

Download PDF sample

Rated 4.19 of 5 – based on 17 votes