Qinlong Wang - Academia.edu (original) (raw)

Papers by Qinlong Wang

Journal of Differential Equations, 2022

Manifolds - Current Research Areas, 2017

In this chapter, by researching the algorithm of the formal series, and deducing the recursion fo... more In this chapter, by researching the algorithm of the formal series, and deducing the recursion formula of computing the nondegenerate and degenerate singular point quantities on center manifold, we investigate the Hopf bifurcation of high-dimensional nonlinear dynamic systems. And more as applications, the singular point quantities for two classes of typical three-or four-dimensional polynomial systems are obtained, the corresponding multiple limit cycles or Hopf cyclicity restricted to the center manifold are discussed.

Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)

Grammatical error correction (GEC) systems strive to correct both global errors in word order and... more Grammatical error correction (GEC) systems strive to correct both global errors in word order and usage, and local errors in spelling and inflection. Further developing upon recent work on neural machine translation, we propose a new hybrid neural model with nested attention layers for GEC. Experiments show that the new model can effectively correct errors of both types by incorporating word and character-level information, and that the model significantly outperforms previous neural models for GEC as measured on the standard CoNLL-14 benchmark dataset. Further analysis also shows that the superiority of the proposed model can be largely attributed to the use of the nested attention mechanism, which has proven particularly effective in correcting local errors that involve small edits in orthography.

Electronic Journal of Qualitative Theory of Differential Equations

We study the isolated periodic wave trains in a class of modified generalized Burgers–Huxley equa... more We study the isolated periodic wave trains in a class of modified generalized Burgers–Huxley equation. The planar systems with a degenerate equilibrium arising after the traveling transformation are investigated. By finding certain positive definite Lyapunov functions in the neighborhood of the degenerate singular points and the Hopf bifurcation points, the number of possible limit cycles in the corresponding planar systems is determined. The existence of isolated periodic wave trains in the equation is established, which is universal for any positive integer n in this model. Within the process, one interesting example is obtained, namely a series of limit cycles bifurcating from a semi-hyperbolic singular point with one zero eigenvalue and one non-zero eigenvalue for its Jacobi matrix.

arXiv: Classical Analysis and ODEs, 2019

In this paper, we give a direct method to study the isochronous centers on center manifolds of th... more In this paper, we give a direct method to study the isochronous centers on center manifolds of three dimensional polynomial differential systems. Firstly, the isochronous constants of the three dimensional system are defined and its recursive formulas are given. The conditions of the isochronous center are determined by the computation of isochronous constants in which it doesn't need compute center manifolds of three dimensional systems. Then the isochronous center conditions of two specific systems are discussed as the applications of our method. The method is an extension and development of the formal series method for the fine focus of planar differential systems and also readily done with using computer algebra system such as Mathematica or Maple.

In this paper, the existence of multiple limit cycles for Chen system are investigated. By using... more In this paper, the existence of multiple limit cycles for Chen system are investigated. By using the method of computing the singular point quantities, the simple and explicit parametric conditions can be determined to the number and stability of multiple limit cycles from Hopf bifurcation. Especially, at least 4 limit cycles can be obtained for the Chen system as a three-dimensional perturbed system.

Mathematical Methods in the Applied Sciences

International Journal of Dynamical Systems and Differential Equations

In this paper, exact wave solutions to the single-species population dynamical model with density... more In this paper, exact wave solutions to the single-species population dynamical model with density-dependent migrations and Allee effect are studied. First, the non-linear evolution equation is reduced to a planar system by transformation of variables, then based on the planar dynamical systems theory, its first integral is determined by computing singular point quantities, and a phase-portrait analysis of its singular points is presented. From this, some explicit expressions of the bounded travelling-wave solutions are obtained for the single-species model, which correspond to the real patterns of spread during biological invasions. In terms of the technique of finding exact travelling-wave solutions of a non-linear partial differential equation, the work is new.

Qualitative Theory of Dynamical Systems

In this paper small amplitude limit cycles and the local bifurcation of critical periods for a qu... more In this paper small amplitude limit cycles and the local bifurcation of critical periods for a quartic Kolmogrov system at the single positive equilibrium point (1, 1) are investigated. Firstly, through the computation of the singular point values, the conditions of the critical point (1, 1) to be a center and to be the highest degree fine singular point are derived respectively. Then, we prove that the maximum number of small amplitude limit cycles bifurcating from the equilibrium point (1, 1) is 7. Furthermore, through the computation of the period constants, the conditions of the critical point (1, 1) to be a weak center of finite order are obtained. Finally, we give respectively that the number of local critical periods bifurcating from the equilibrium point (1, 1) under the center conditions. It is the first example of a quartic Kolmogorov system with seven limit cycles and a quartic Kolmogorov system with four local critical periods created from a single positive equilibrium point.

Journal of Applied Mathematics, 2014

We discuss the complex isochronicity of a sixth degree polynomial system. We first adopt a new al... more We discuss the complex isochronicity of a sixth degree polynomial system. We first adopt a new algorithm to find necessary conditions for complex isochronicity, then we derive sufficient conditions.

Applied Mathematics and Computation, 2014

ABSTRACT For Lorenz system we investigate multiple Hopf bifurcation and center-focus problem of i... more ABSTRACT For Lorenz system we investigate multiple Hopf bifurcation and center-focus problem of its equilibria. By applying the method of symbolic computation, we obtain the first three singular point quantities. It is proven that Lorenz system can generate 3 small limit cycles from each of the two symmetric equilibria. Furthermore, the center conditions are found and as weak foci the highest order is proved to be the third, thus we obtain at most 6 small limit cycles from the symmetric equilibria via Hopf bifurcation. At the same time, we realize also that though the same for the related three-dimensional chaotic systems, Lorenz system differs in Hopf bifurcation greatly from the Chen system and Lü system.

Applied Mathematics Letters, 2014

ABSTRACT In this paper, we consider a class of biological invasion model with density-dependent m... more ABSTRACT In this paper, we consider a class of biological invasion model with density-dependent migrations and Allee effect, which is reduced to one ordinary differential form via the travelling wave solution ansatz. For the corresponding planar system, we firstly obtain the first several weak focal values of its one equilibrium by computing the singular point quantities, then determine the existence of one stable limit cycle from its Hopf bifurcation. Thus a special periodic travelling wave solution which is isolate as a limit is obtained, and it corresponds to the particular real patterns of spread during biological invasions, which is an interesting discovery.

International Journal of Bifurcation and Chaos, 2014

Chemical Communications, 2011

Blue luminescent reduced state carbon dots were prepared by reducing carbon dots with NaBH(4). Th... more Blue luminescent reduced state carbon dots were prepared by reducing carbon dots with NaBH(4). The quantum yield of the reduced state carbon dots increased from 2% to 24% and the maximum emission wavelength shifted from 520 to 450 nm. This offers a simple pathway to enhance the luminescence of carbon dots.