Advances in Mathematical Physics

Theoretical and Computational Advances in Nonlinear Dynamical Systems


Status
Published

Lead Editor

1Technion-Israel Institute of Technology, Haifa, Israel

2University of Massachusetts Amherst, Amherst, USA

3Beihang University, Beijing, China

4University of Aberdeen, Aberdeen, UK


Theoretical and Computational Advances in Nonlinear Dynamical Systems

Description

The theory of dynamical systems is the paradigm for studying various scientific phenomena, ranging from complex atomic lattices to planetary motion, from water waves to weather systems, from chemical reaction to biological behaviors, and so forth. Application of dynamical systems has widely arisen in the multidisciplinary fields including mathematics, physics, chemistry, biology, and even economy and sociology.

In recent years, due to rapid development of theoretical and computational techniques, the nonlinear dynamical systems have attracted increasing volume of interest, where nonlinearity plays the heart role of many interesting dynamical behaviors. A typical research area is the spatial and temporary evolution of the localized structures for various nonlinear dynamical systems, such as solitons and vortices. Motion of these localized structures, as well as their interactions, reflects the triggering features for the nonlinear dynamical systems, being discussed in the condensed matter physics, fluidic media, solid lattices, and many relevant areas. Meanwhile, the mathematical tools, including the analytical and numerical aspects, have been developed in dealing with the nonlinear dynamical systems qualitatively and quantitatively.

Complexity of the nonlinear dynamical systems can be further revealed when chaotic and stochastic behaviors are considered. For instance, interactions between nonlinearity and randomness are highlight topics nowadays, emerging from soliton dynamics in random media to destruction of the Anderson localization by nonlinearity. Thanks to the rapid development of computer resources, these complex phenomena for the nonlinear dynamical systems can be simulated and studied in relevant scientific communities.

Potential topics include but are not limited to the following:

  • Nonlinear dynamics of continuous, discrete, and hybrid systems
  • Integral equations and applications
  • Symmetry and conservation laws for nonlinear PDEs
  • Solitons and vortices and their interactions
  • Chaos, resonances, and stability analysis in nonlinear systems
  • Interplay of nonlinearity and randomness for dynamical systems
  • Symbolic and numerical methods
  • Fluid dynamics, nonlinear optics, and Bose-Einstein condensates

Articles

  • Special Issue
  • - Volume 2017
  • - Article ID 3925964
  • - Editorial

Theoretical and Computational Advances in Nonlinear Dynamical Systems

Zhi-Yuan Sun | Panayotis G. Kevrekidis | ... | K. Nakkeeran
  • Special Issue
  • - Volume 2017
  • - Article ID 9736818
  • - Research Article

Error Estimates on Hybridizable Discontinuous Galerkin Methods for Parabolic Equations with Nonlinear Coefficients

Minam Moon | Hyung Kyu Jun | Tay Suh
  • Special Issue
  • - Volume 2017
  • - Article ID 5214616
  • - Research Article

The Spreading Residue Harmonic Balance Method for Strongly Nonlinear Vibrations of a Restrained Cantilever Beam

Y. H. Qian | J. L. Pan | ... | M. H. Yao
  • Special Issue
  • - Volume 2017
  • - Article ID 2717352
  • - Research Article

Computation of the Stability and Complexity about Triopoly Price Game Model with Delay Decision

Yuling Wang | Shubing Guo | Shide Duan
  • Special Issue
  • - Volume 2017
  • - Article ID 5865403
  • - Research Article

Application of Adjoint Data Assimilation Method to Atmospheric Aerosol Transport Problems

Minjie Xu | Kai Fu | Xianqing Lv
  • Special Issue
  • - Volume 2017
  • - Article ID 1843179
  • - Research Article

Adaptive Modified Function Projective Lag Synchronization of Memristor-Based Five-Order Chaotic Circuit Systems

Qiaoping Li | Sanyang Liu
  • Special Issue
  • - Volume 2017
  • - Article ID 5210708
  • - Research Article

Numerical Simulations of the Square Lid Driven Cavity Flow of Bingham Fluids Using Nonconforming Finite Elements Coupled with a Direct Solver

R. Mahmood | N. Kousar | ... | K. Jabeen
  • Special Issue
  • - Volume 2017
  • - Article ID 6976205
  • - Research Article

The Convergence Ball and Error Analysis of the Relaxed Secant Method

Rongfei Lin | Qingbiao Wu | ... | Lu Liu
  • Special Issue
  • - Volume 2017
  • - Article ID 9648538
  • - Research Article

Turing Bifurcation and Pattern Formation of Stochastic Reaction-Diffusion System

Qianiqian Zheng | Zhijie Wang | ... | Hussain Muhammad Ather Iqbal
  • Special Issue
  • - Volume 2017
  • - Article ID 3094173
  • - Research Article

The General Solution of Differential Equations with Caputo-Hadamard Fractional Derivatives and Noninstantaneous Impulses

Xianzhen Zhang | Zuohua Liu | ... | Shiyong Yang
Advances in Mathematical Physics
 Journal metrics
Acceptance rate24%
Submission to final decision37 days
Acceptance to publication39 days
CiteScore1.300
Impact Factor1.130
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