American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Qualitative analysis of an age- and sex-structured vaccination model for human papillomavirus
  • DCDS-B Home
  • This Issue
  • Next Article
    Permanence of a general discrete-time two-species-interaction model with nonlinear per-capita growth rates
October  2013, 18(8): 2143-2149. doi: 10.3934/dcdsb.2013.18.2143

A note on global asymptotic stability of nonautonomous master equations

Christian Lax 1, and  Sebastian Walcher 2,

1. 

Lehrstuhl A für Mathematik, RWTH Aachen, D-52056 Aachen, Germany
2. 

Lehrstuhl A für Mathematik, RWTH Aachen, 52056 Aachen

Received  March 2013 Revised  May 2013 Published  July 2013

We present sufficient conditions to either preclude or guarantee global asymptotic stability of linear differential equations for time-dependent $\mathbb W$-matrices. These conditions are concerned with integrability or non-integrability of the matrix entries. The proofs employ differential inequalities.
Keywords: Stability, integrability, convergence, differential inequality., stochastic matrix.
Mathematics Subject Classification: Primary: 34D05, 34D23; Secondary: 37B5.
Citation: Christian Lax, Sebastian Walcher. A note on global asymptotic stability of nonautonomous master equations. Discrete & Continuous Dynamical Systems - B, 2013, 18 (8) : 2143-2149. doi: 10.3934/dcdsb.2013.18.2143
References:
[1]

A. Berman and R. J. Plemmons, "Nonnegative Matrices in the Mathematical Sciences," Computer Science and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1979.  Google Scholar

[2]

B. A. Earnshaw and J. P. Keener, Global asymptotic stability of solutions of nonautonomous master equations, SIAM J. Applied Dynamical Systems, 9 (2010), 220-237. doi: 10.1137/090763421.  Google Scholar

[3]

N. G. van Kampen, "Stochastic Processes in Physics and Chemistry," Lecture Notes in Mathematics, 888, North-Holland Publishing Co., Amsterdam-New York, 1981.  Google Scholar

[4]

W. Walter, "Gewöhnliche Differentialgleichungen," 7. Aufl., Springer-Verlag, Berlin, 2000. Google Scholar

show all references

References:
[1]

A. Berman and R. J. Plemmons, "Nonnegative Matrices in the Mathematical Sciences," Computer Science and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1979.  Google Scholar

[2]

B. A. Earnshaw and J. P. Keener, Global asymptotic stability of solutions of nonautonomous master equations, SIAM J. Applied Dynamical Systems, 9 (2010), 220-237. doi: 10.1137/090763421.  Google Scholar

[3]

N. G. van Kampen, "Stochastic Processes in Physics and Chemistry," Lecture Notes in Mathematics, 888, North-Holland Publishing Co., Amsterdam-New York, 1981.  Google Scholar

[4]

W. Walter, "Gewöhnliche Differentialgleichungen," 7. Aufl., Springer-Verlag, Berlin, 2000. Google Scholar

[1]

Graeme D. Chalmers, Desmond J. Higham. Convergence and stability analysis for implicit simulations of stochastic differential equations with random jump magnitudes. Discrete & Continuous Dynamical Systems - B, 2008, 9 (1) : 47-64. doi: 10.3934/dcdsb.2008.9.47
[2]

Yulan Lu, Minghui Song, Mingzhu Liu. Convergence rate and stability of the split-step theta method for stochastic differential equations with piecewise continuous arguments. Discrete & Continuous Dynamical Systems - B, 2019, 24 (2) : 695-717. doi: 10.3934/dcdsb.2018203
[3]

Giuseppe Da Prato. An integral inequality for the invariant measure of some finite dimensional stochastic differential equation. Discrete & Continuous Dynamical Systems - B, 2016, 21 (9) : 3015-3027. doi: 10.3934/dcdsb.2016085
[4]

Jun Zhou, Jun Shen, Weinian Zhang. A powered Gronwall-type inequality and applications to stochastic differential equations. Discrete & Continuous Dynamical Systems, 2016, 36 (12) : 7207-7234. doi: 10.3934/dcds.2016114
[5]

Liping Pang, Fanyun Meng, Jinhe Wang. Asymptotic convergence of stationary points of stochastic multiobjective programs with parametric variational inequality constraint via SAA approach. Journal of Industrial & Management Optimization, 2019, 15 (4) : 1653-1675. doi: 10.3934/jimo.2018116
[6]

Yun Cai, Song Li. Convergence and stability of iteratively reweighted least squares for low-rank matrix recovery. Inverse Problems & Imaging, 2017, 11 (4) : 643-661. doi: 10.3934/ipi.2017030
[7]

Zhuchun Li, Yi Liu, Xiaoping Xue. Convergence and stability of generalized gradient systems by Łojasiewicz inequality with application in continuum Kuramoto model. Discrete & Continuous Dynamical Systems, 2019, 39 (1) : 345-367. doi: 10.3934/dcds.2019014
[8]

Bahareh Akhtari, Esmail Babolian, Andreas Neuenkirch. An Euler scheme for stochastic delay differential equations on unbounded domains: Pathwise convergence. Discrete & Continuous Dynamical Systems - B, 2015, 20 (1) : 23-38. doi: 10.3934/dcdsb.2015.20.23
[9]

Tomás Caraballo, José Real, T. Taniguchi. The exponential stability of neutral stochastic delay partial differential equations. Discrete & Continuous Dynamical Systems, 2007, 18 (2&3) : 295-313. doi: 10.3934/dcds.2007.18.295
[10]

Min Zhu, Panpan Ren, Junping Li. Exponential stability of solutions for retarded stochastic differential equations without dissipativity. Discrete & Continuous Dynamical Systems - B, 2017, 22 (7) : 2923-2938. doi: 10.3934/dcdsb.2017157
[11]

Jaume Llibre, Claudia Valls. On the analytic integrability of the Liénard analytic differential systems. Discrete & Continuous Dynamical Systems - B, 2016, 21 (2) : 557-573. doi: 10.3934/dcdsb.2016.21.557
[12]

Jaume Llibre, Claudia Valls. Analytic integrability of a class of planar polynomial differential systems. Discrete & Continuous Dynamical Systems - B, 2015, 20 (8) : 2657-2661. doi: 10.3934/dcdsb.2015.20.2657
[13]

Bin Pei, Yong Xu, Yuzhen Bai. Convergence of p-th mean in an averaging principle for stochastic partial differential equations driven by fractional Brownian motion. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 1141-1158. doi: 10.3934/dcdsb.2019213
[14]

Chuchu Chen, Jialin Hong. Mean-square convergence of numerical approximations for a class of backward stochastic differential equations. Discrete & Continuous Dynamical Systems - B, 2013, 18 (8) : 2051-2067. doi: 10.3934/dcdsb.2013.18.2051
[15]

Junhao Hu, Chenggui Yuan. Strong convergence of neutral stochastic functional differential equations with two time-scales. Discrete & Continuous Dynamical Systems - B, 2019, 24 (11) : 5831-5848. doi: 10.3934/dcdsb.2019108
[16]

Angelo B. Mingarelli. Nonlinear functionals in oscillation theory of matrix differential systems. Communications on Pure & Applied Analysis, 2004, 3 (1) : 75-84. doi: 10.3934/cpaa.2004.3.75
[17]

Brigita Ferčec, Valery G. Romanovski, Yilei Tang, Ling Zhang. Integrability and bifurcation of a three-dimensional circuit differential system. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021243
[18]

S. J. Li, Z. M. Fang. On the stability of a dual weak vector variational inequality problem. Journal of Industrial & Management Optimization, 2008, 4 (1) : 155-165. doi: 10.3934/jimo.2008.4.155
[19]

Parikshit Upadhyaya, Elias Jarlebring, Emanuel H. Rubensson. A density matrix approach to the convergence of the self-consistent field iteration. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 99-115. doi: 10.3934/naco.2020018
[20]

Yong Ren, Xuejuan Jia, Lanying Hu. Exponential stability of solutions to impulsive stochastic differential equations driven by $G$-Brownian motion. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 2157-2169. doi: 10.3934/dcdsb.2015.20.2157

2020 Impact Factor: 1.327

Tools

Metrics

  • PDF downloads (51)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences | Privacy Policy