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发表于 2025-3-21 19:52:52
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BRIDE
发表于 2025-3-21 23:50:34
Periodic solutions,The concept of a periodic solution of a differential equation was introduced in section 2.3. We have shown that in the case of an autonomous equation the periodic solutions correspond with closed orbits in phase-space.
Endearing
发表于 2025-3-22 03:40:32
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osteopath
发表于 2025-3-22 07:37:23
Introduction to perturbation theory,This chapter is intended as an introduction for those readers who are not aquainted with the basics of perturbation theory. In that case it serves in preparing for the subsequent chapters.
施加
发表于 2025-3-22 09:38:04
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BLOT
发表于 2025-3-22 14:21:14
Relaxation oscillations,Relaxation oscillations are periodic phenomena with very special features during a period. The characteristics can be illustrated by the following mechanical system.
landfill
发表于 2025-3-22 17:56:09
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Flinch
发表于 2025-3-22 21:39:24
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无节奏
发表于 2025-3-23 02:07:13
Stability by linearisation,pecial solutions. In section 5.4 we have discussed linearisation and we have given a summary of the analysis of linear systems. These methods have been in use for a long time but only since around 1900 the justification of linearisation methods has been started by Poincaré and Lyapunov.
TIA742
发表于 2025-3-23 06:22:05
Stability analysis by the direct method,eceding chapter. When linearising one starts off with small perturbations of the equilibrium or periodic solution and one studies the effect of these . perturbations. In the so-called direct method one characterises the solution in a way with respect to stability which is not necessarily local.