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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Geometric Singular Perturbation Theory and Traveling Pulses with Monotone Tails in a Diffusive Rosenzweig MacArthur Model
扩散 罗森茨威格麦克阿瑟模型 几何奇异摄动理论 单调尾巴行进脉冲
2023/5/5
In this talk, we first briefly review history of the geometric singular perturbation theory, then talk about the traveling pulses for a diffusive Rosenzweig MacArthur model. We show the existence of t...
The thin film equation with non zero contact angle:A singular perturbation approach
thin film equation non zero contact angle singular perturbation approach
2015/10/15
In this paper we prove the existence of weak solutions for the thin film equation with prescribed non zero contact angle and for a large class of mobility coefficients, in dimension 1. The existence o...
Regular perturbation of V -geometrically ergodic Markov chains
Regular perturbation V -geometrically ergodic Markov chains Probability
2012/6/21
In this paper, new conditions for the stability of V-geometrically ergodic Markov chains are introduced. The results are based on an extension of the standard perturbation theory formulated by Keller ...
Witten's perturbation on strata
Morse inequalities ideal boundary condition Thom-Mather stratification Witten’s perturbation
2012/5/24
The main result is a version of Morse inequalities for the minimum and maximum ideal boundary conditions of the de Rham complex on strata of compact Thom-Mather stratifications, endowed with adapted m...
Approximate Solution of the Singular-Perturbation Problem on Chebyshev-Gauss Grid
Singular Perturbation Problems Two-Point Boundary Value Problems The Shifted Chebyshev Polynomials Approximation Method Matrix Method
2013/1/30
Matrix methods, now-a-days, are playing an important role in solving the real life problems governed by ODEs and/or by PDEs. Many differential models of sciences and engineers for which the existing m...
Exponentially and non-exponentially small splitting of separatrices for the pendulum with a fast meromorphic perturbation
non-exponentially small splitting fast meromorphic perturbation Dynamical Systems
2011/9/29
Abstract: In this paper we study the splitting of separatrices phenomenon which arises when one considers a Hamiltonian System of one degree of freedom with a fast periodic or quasiperiodic and meromo...
Singular Perturbation Approximations for a Class of Linear Quantum Systems
Singular Perturbation Approximations Linear Quantum Systems Optimization and Control
2011/10/10
Abstract: This paper considers the use of singular perturbation approximations for a class of linear quantum systems arising in the area of linear quantum optics. The paper presents results on the phy...
Moderate Deviation Principle for dynamical systems with small random perturbation
Freidlin-Wentzell’s theorem large deviations moderate deviations Talagrand’s transportation inequality
2011/9/14
Abstract: Consider the stochastic differential equation in $\rr^d$
dX^{\e}_t&=b(X^{\e}_t)dt+\sqrt{\e}\sigma(X^\e_t)dB_t
X^{\e}_0&=x_0,\quad x_0\in\rr^d
where $b:\rr^d\rightarrow\rr^d$ is $C^1$ s...
Perturbation approach to multifractal dimensions for certain critical random matrix ensembles
multifractal dimensions Perturbation random matrix ensembles
2011/7/6
Fractal dimensions of eigenfunctions for various critical random matrix ensembles are investigated in perturbation series in the regimes of strong and weak multifractality. In both regimes we obtain e...
A note on Gornik's perturbation of Khovanov-Rozansky homology
note Gornik's perturbation Khovanov-Rozansky homology
2011/1/21
We show that the information contained in the associated graded vector space to Gornik’s version of Khovanov-Rozansky knot homology is equivalent to a single even integer sn(K). Furthermore we show th...
Homotopy perturbation method for Chebyshev and Legendre equations
Homotopy Perturbation Method Ordinary Differential Equations
2010/9/26
In this paper, we implement the Homotopy Perturbation Method to obtain the solutions of Chebyshev and Legendre differential equations. The exact solution will be find by constructing an efficient homo...
We study the effect of a random perturbation on a one-parameter family of dynamical systems whose behavior in the absence of perturbation is ill understood.We provide conditions under which the pertur...
Positive Lyapunov exponent by a random perturbation
Lyapunov exponent random perturbation
2010/12/28
We study the effect of a random perturbation on a one-parameter family of dynamical systems whose behavior in the absence of perturbation is ill understood.We provide conditions under which the pertur...
Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation
Dirichlet heat kernel fractional Laplacian gradient perturbation
2010/11/19
Suppose $d\geq 2$ and $\alpha \in (1, 2)$. Let $D$ be a bounded $C^{1,1}$ open set in $R^d$ and $b$ an $R^d$-valued function on $R^d$ whose components are in a certain Kato class of the rotationally ...
Homotopy perturbation Pade technique for constructing approximate and exact solutions of Boussinesq equations
Homotopy perturbation method Padé approximants
2010/9/13
Based on the homotopy perturbation method (HPM) and Padé approximants (PA), explicit approximate and exact solutions are obtained for cubic Boussinesq equations. HPM is used for analytic treatment to ...