• Corpus ID: 236429121

Surprises in a classic boundary-layer problem

@inproceedings{Clark2021SurprisesIA,
  title={Surprises in a classic boundary-layer problem},
  author={William A. Clark and Mario W. Gomes and Arnaldo Rodriguez-Gonzalez and Leo C. Stein and Steven H. Strogatz},
  year={2021}
}
We revisit a textbook example of a singularly perturbed nonlinear boundary-value problem. Unexpectedly, it shows a wealth of phenomena that seem to have been overlooked previously, including a pitchfork bifurcation in the number of solutions as one varies the small parameter, and transcendentally small terms in the initial conditions that can be calculated by elementary means. Based on our own classroom experience, we believe this problem could provide an enjoyable workout for students in… 

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References

SHOWING 1-10 OF 24 REFERENCES

Bifurcation of solutions to Hamiltonian boundary value problems

A bifurcation is a qualitative change in a family of solutions to an equation produced by varying parameters. In contrast to the local bifurcations of dynamical systems that are often related to a

Introduction to Perturbation Methods

TLDR
The WKB and Related Methods are described and the method of Homogenization is explained, followed by a discussion of the properties of Transition Layer Equations and asymptotic approximations.

Extending Geometric Singular Perturbation Theory to Nonhyperbolic Points - Fold and Canard Points in Two Dimensions

TLDR
This work presents a method based on blow-up techniques, which leads to a rigorous geometric analysis of the extension of slow manifolds past fold points and canard points in planar systems.

Advanced mathematical methods for scientists and engineers I: asymptotic methods and perturbation theory.

TLDR
Eventually, you will enormously discover a supplementary experience and execution by Spending more cash by spending more cash.

Multiple Scale and Singular Perturbation Methods

1. Introduction.- 1.1. Order Symbols, Uniformity.- 1.2. Asymptotic Expansion of a Given Function.- 1.3. Regular Expansions for Ordinary and Partial Differential Equations.- References.- 2. Limit

Weakly Nonlocal Solitary Waves and Beyond-All-Orders Asymptotics

Preface. Part I: Overview. 1. Introduction. Part II: Analytical Methods. 2. The Method of Multiple Scales and The epsilon-Power Series. 3. Hyperasymptotic Perturbation Theory. 4. Matched Asymptotic

Matched Asymptotic Expansions: Ideas and Techniques

I. Introduction: General Concepts of Singular Perturbation Theory.- II. Layer-type Problems. Ordinary Differential Equations.- III. Layer-type Problems. Partial Differential Equations.- List of

The canard unchainedor how fast/slow dynamical systems bifurcate

On Fast–Slow Consensus Networks with a Dynamic Weight

TLDR
It is shown that, under mild conditions on the weight, there exists a reduction such that the dynamics of the network are organized by a transcritical singularity, and it is observed that an exchange between consensus and clustering of the nodes is possible.

Perturbation Methods

TLDR
This website becomes a very available place to look for countless perturbation methods sources and sources about the books from countries in the world are provided.