# American Institute of Mathematical Sciences

December  2015, 8(6): i-ii. doi: 10.3934/dcdss.2015.8.6i

## New trends on nonlinear dynamics and its applications

 1 Dpto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Campus Reina Mercedes, Apdo. de Correos 1160, 41080 Sevilla 2 Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Hospital de Marina, 30203-Cartagena, Región de Murcia, Spain

Published  December 2015

Nonlinear Dynamics and Complexity is a wide area of research which is experiencing a big development nowadays. For this reason, we thought that it could be very helpful to publish a theme issue which could provide an overview of the recent developments, discoveries and progresses on this fascinating field of Nonlinear Dynamics and Complexity. Therefore, the main aims of this issue are to present the fundamental and frontier theories and techniques for modern science and technology which can also stimulate more research interest for exploration of nonlinear science and complexity and, to directly pass the new knowledge to the young generation, engineers and technologists in the corresponding fields. Consequently, the contributions which have been accepted for this issue focus on recent developments, findings and progresses on fundamental theories and principles, analytical and symbolic approaches, computational techniques in nonlinear physical science and nonlinear mathemati cs. Amongst others, the main topics of interest in Nonlinear Dynamics and Complexity treated in these papers include, but are not limited to:

Citation: Tomás Caraballo, Juan L. G. Guirao. New trends on nonlinear dynamics and its applications. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : i-ii. doi: 10.3934/dcdss.2015.8.6i
 [1] E. B. Dynkin. A new inequality for superdiffusions and its applications to nonlinear differential equations. Electronic Research Announcements, 2004, 10: 68-77. [2] Rosa M. Benito, Regino Criado, Juan C. Losada, Miguel Romance. Preface: "New trends, models and applications in complex and multiplex networks". Networks & Heterogeneous Media, 2015, 10 (1) : i-iii. doi: 10.3934/nhm.2015.10.1i [3] Abdon Atangana, Zakia Hammouch, Kolade M. Owolabi, Gisele Mephou. Preface: New trends on numerical analysis and analytical methods with their applications to real world problems. Discrete & Continuous Dynamical Systems - S, 2019, 12 (3) : ⅰ-ⅰ. doi: 10.3934/dcdss.201903i [4] Ming Huang, Cong Cheng, Yang Li, Zun Quan Xia. The space decomposition method for the sum of nonlinear convex maximum eigenvalues and its applications. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-21. doi: 10.3934/jimo.2019034 [5] Aviv Gibali, Dang Thi Mai, Nguyen The Vinh. A new relaxed CQ algorithm for solving split feasibility problems in Hilbert spaces and its applications. Journal of Industrial & Management Optimization, 2019, 15 (2) : 963-984. doi: 10.3934/jimo.2018080 [6] Luis A. Caffarelli, Alexis F. Vasseur. The De Giorgi method for regularity of solutions of elliptic equations and its applications to fluid dynamics. Discrete & Continuous Dynamical Systems - S, 2010, 3 (3) : 409-427. doi: 10.3934/dcdss.2010.3.409 [7] Giovanni Forni, Carlos Matheus. Introduction to Teichmüller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards. Journal of Modern Dynamics, 2014, 8 (3&4) : 271-436. doi: 10.3934/jmd.2014.8.271 [8] Xilin Fu, Zhang Chen. New discrete analogue of neural networks with nonlinear amplification function and its periodic dynamic analysis. Conference Publications, 2007, 2007 (Special) : 391-398. doi: 10.3934/proc.2007.2007.391 [9] Shaobo Lin, Xingping Sun, Zongben Xu. Discretizing spherical integrals and its applications. Conference Publications, 2013, 2013 (special) : 499-514. doi: 10.3934/proc.2013.2013.499 [10] Kyoungsun Kim, Gen Nakamura, Mourad Sini. The Green function of the interior transmission problem and its applications. Inverse Problems & Imaging, 2012, 6 (3) : 487-521. doi: 10.3934/ipi.2012.6.487 [11] Jinchao Xu. The single-grid multilevel method and its applications. Inverse Problems & Imaging, 2013, 7 (3) : 987-1005. doi: 10.3934/ipi.2013.7.987 [12] Hui Ma, Dongxu Qi, Ruixia Song, Tianjun Wang. The complete orthogonal V-system and its applications. Communications on Pure & Applied Analysis, 2007, 6 (3) : 853-871. doi: 10.3934/cpaa.2007.6.853 [13] Xian-gao Liu, Xiaotao Zhang. Liouville theorem for MHD system and its applications. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2329-2350. doi: 10.3934/cpaa.2018111 [14] Yuanzhen Shao. Continuous maximal regularity on singular manifolds and its applications. Evolution Equations & Control Theory, 2016, 5 (2) : 303-335. doi: 10.3934/eect.2016006 [15] Peng Gao. Global Carleman estimate for the Kawahara equation and its applications. Communications on Pure & Applied Analysis, 2018, 17 (5) : 1853-1874. doi: 10.3934/cpaa.2018088 [16] Joshua Du, Jun Ji. An integral representation of the determinant of a matrix and its applications. Conference Publications, 2005, 2005 (Special) : 225-232. doi: 10.3934/proc.2005.2005.225 [17] James Kingsbery, Alex Levin, Anatoly Preygel, Cesar E. Silva. Dynamics of the $p$-adic shift and applications. Discrete & Continuous Dynamical Systems - A, 2011, 30 (1) : 209-218. doi: 10.3934/dcds.2011.30.209 [18] Jianqing Chen. Best constant of 3D Anisotropic Sobolev inequality and its applications. Communications on Pure & Applied Analysis, 2010, 9 (3) : 655-666. doi: 10.3934/cpaa.2010.9.655 [19] Valerii Los, Vladimir A. Mikhailets, Aleksandr A. Murach. An isomorphism theorem for parabolic problems in Hörmander spaces and its applications. Communications on Pure & Applied Analysis, 2017, 16 (1) : 69-98. doi: 10.3934/cpaa.2017003 [20] Lei Qiao. Asymptotic behaviors of Green-Sch potentials at infinity and its applications. Discrete & Continuous Dynamical Systems - B, 2017, 22 (6) : 2321-2338. doi: 10.3934/dcdsb.2017099

2018 Impact Factor: 0.545