Poincaré maps for multiscale physics discovery and nonlinear Floquet theory
نویسندگان
چکیده
منابع مشابه
Floquet Theory and Stability of Nonlinear Integro-differential Equations
One of the classical topics in the qualitative theory of differential equations is the Floquet theory. It provides a means to represent solutions and helps in particular for stability analysis. In this paper first we shall study Floquet theory for integro-differential equations (IDE), and then employ it to address stability problems for linear and nonlinear equations.
متن کاملFloquet Theory
Lemma 8.4 If C is a n n × matrix with 0 det ≠ C , then, there exists a n n × (complex) matrix B such that C e = . Proof: For any matrix C , there exists an invertible matrix P , s.t. 1 P CP J − = , where J is a Jordan matrix. If C e = , then, 1 1 1 P B P B e P e P P CP J − − − = = = . Therefore, it is suffice to prove the result when C is in a canonical form. Suppose that 1 ( , , ) s C diag C C...
متن کاملMultiscale Homogenization in Kirchhoff’s Nonlinear Plate Theory
The interplay between multiscale homogenization and dimension reduction for nonlinear elastic thin plates is analyzed in the case in which the scaling of the energy corresponds to Kirchhoff’s nonlinear bending theory for plates. Different limit models are deduced depending on the relative ratio between the thickness parameter h and the two homogenization scales ε and ε.
متن کاملAbstract booklet for Nonlinear Physics: Theory and Experiment. III
booklet for Nonlinear Physics: Theory and Experiment. III Gallipoli (Lecce, Italy) 24 June – 3 July 2004 Information received within June 15, 2004 —————————————————————————————Mark J. Ablowitz Department of Applied Mathematics, University of Colorado UCB 526, Boulder 80309 CO Chazy-Darboux-Halphen Systems At the turn of the last century Painlevé and his school obtained a class of ordinary diffe...
متن کاملLinear theory for filtering nonlinear multiscale systems with model error.
In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physica D: Nonlinear Phenomena
سال: 2020
ISSN: 0167-2789
DOI: 10.1016/j.physd.2020.132479