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Special issue on stability and complexity of differential systems

David Cheban, School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China; State University of Moldova, Faculty of Mathematics and Informatics, Department of Mathematics, A. Mateevich Street 60, MD--2009 Chişinău, Moldova cheban@usm.md
Wen Huang, CAS Wu Wen-Tsun Key Laboratory of Mathematics, and Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China wenh@mail.ustc.edu.cn
Zhenxin Liu, School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China zxliu@dlut.edu.cn

Averaging principle on infinite intervals for stochastic ordinary differential equationsSpecial Issues
David Cheban and Zhenxin Liu
2021, 29(4): 2791-2817 doi: 10.3934/era.2021014 +[Abstract](349)+[HTML](157) +[PDF](410.94KB)

In contrast to existing works on stochastic averaging on finite intervals, we establish an averaging principle on the whole real axis, i.e. the so-called second Bogolyubov theorem, for semilinear stochastic ordinary differential equations in Hilbert space with Poisson stable (in particular, periodic, quasi-periodic, almost periodic, almost automorphic etc) coefficients. Under some appropriate conditions we prove that there exists a unique recurrent solution to the original equation, which possesses the same recurrence property as the coefficients, in a small neighborhood of the stationary solution to the averaged equation, and this recurrent solution converges to the stationary solution of averaged equation uniformly on the whole real axis when the time scale approaches zero.

Ergodic measures of intermediate entropy for affine transformations of nilmanifoldsSpecial Issues
Wen Huang, Leiye Xu and Shengnan Xu
2021, 29(4): 2819-2827 doi: 10.3934/era.2021015 +[Abstract](299)+[HTML](167) +[PDF](330.89KB)

In this paper we study ergodic measures of intermediate entropy for affine transformations of nilmanifolds. We prove that if an affine transformation \begin{document}$ \tau $\end{document} of nilmanifold has a periodic point, then for every \begin{document}$ a\in[0, h_{top}(\tau)] $\end{document} there exists an ergodic measure \begin{document}$ \mu_a $\end{document} of \begin{document}$ \tau $\end{document} such that \begin{document}$ h_{\mu_a}(\tau) = a $\end{document}.

Instability and bifurcation of a cooperative system with periodic coefficientsSpecial Issues
Tian Hou, Yi Wang and Xizhuang Xie
2021, 29(5): 3069-3079 doi: 10.3934/era.2021026 +[Abstract](15)+[HTML](11) +[PDF](807.77KB)
Simultaneous recovery of surface heat flux and thickness of a solid structure by ultrasonic measurementsSpecial Issues
Youjun Deng, Hongyu Liu, Xianchao Wang, Dong Wei and Liyan Zhu
2021, 29(5): 3081-3096 doi: 10.3934/era.2021027 +[Abstract](15)+[HTML](11) +[PDF](525.34KB)
On the existence of solutions for the Frenkel-Kontorova models on quasi-crystalsSpecial Issues
Jianxing Du and Xifeng Su
2021, 29(6): 4177-4198 doi: 10.3934/era.2021078 +[Abstract](15)+[HTML](11) +[PDF](642.28KB)

2020 Impact Factor: 1.833
5 Year Impact Factor: 1.833



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