Titlebook: Singular Perturbations; Introduction to Syst Elena Shchepakina,Vladimir Sobolev,Michael P. Mort Book 2014 Springer International Publishing

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Representations of Slow Integral Manifolds,e explicitly. In many problems this is not possible due to the fact that the degenerate equation is either a high degree polynomial or transcendental. In this situation many authors suggest the use of numerical methods. However, in many problems the slow surface can be described in parametric form,

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Singular Singularly Perturbed Systems,e, the standard theory to establish a slow integral manifold near this solution does not work. Applying scaling transformations and using the technique of gauge functions we reduce the original singularly perturbed problem to a regularized one such that the existence of slow integral manifolds can b

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Specific Cases,en the main hypothesis is violated, i.e., when the real parts of some or all of the eigenvalues of the matrix of the linearized fast subsystem are no longer strictly negative. This means that the hypotheses of the Tikhonov’s theorem are violated. This chapter is organized as follows. The first secti

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Canards and Black Swans,tical phenomena in chemical kinetics. We consider different problems e.g., laser models, classical combustion models and gas combustion in a dust-laden medium models, 3-D autocatalator model, using the techniques of canards and black swans. The existence of canard cascades is stated for the van der

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Lecture Notes in Mathematicshttp://image.papertrans.cn/s/image/867897.jpg

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https://doi.org/10.1007/978-3-319-09570-7Black Swans; Canards; Chemical Kinetics; Combustion and Explosion; Enzyme Kinetics; Integral Manifolds; In

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Appendix: Proofs,In this chapter we give the proof of a number of assertions from previous chapters. The level of mathematical sophistication required of the reader is higher than earlier chapters. For this reason, and if the readers’ primary interest is in the application of the techniques, this chapter may be skipped.

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Elena Shchepakina,Vladimir Sobolev,Michael P. MortBegins with the basics and moves in easy stages, up to dealing with research level problems.Explains the theory as well as providing fresh examples and applications.Emphasises slow integral manifolds

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