ISSN:
 1937-1632

eISSN:
 1937-1179

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Volume 14, 2021

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Discrete & Continuous Dynamical Systems - S

Open Access Articles

Preface
Michal Beneš, Tetsuya Ishiwata, Masato Kimura and Shigetoshi Yazaki
2021, 14(3): ⅰ-ⅰ doi: 10.3934/dcdss.2021009 +[Abstract](215) +[HTML](107) +[PDF](68.56KB)
Abstract:
Preface
M. Liero, S. Reichelt, G. Schneider, F. Theil and M. Thomas
2021, 14(1): i-iv doi: 10.3934/dcdss.2020455 +[Abstract](263) +[HTML](71) +[PDF](109.85KB)
Abstract:
Preface to this special issue
Genni Fragnelli, Jerome A. Goldstein and Alain Miranville
2020, 13(12): i-ii doi: 10.3934/dcdss.2020422 +[Abstract](402) +[HTML](183) +[PDF](98.87KB)
Abstract:
Preface: Recent advances in bifurcation theory and application
Jingli Ren and Gail S. K. Wolkowicz
2020, 13(11): i-ii doi: 10.3934/dcdss.2020417 +[Abstract](653) +[HTML](141) +[PDF](91.57KB)
Abstract:
Special issue dedicated to Professor David Paul Mason
Chaudry Masood Khalique, Muhammad Usman and Maria Luz Gandarais
2020, 13(10): iii-iv doi: 10.3934/dcdss.2020416 +[Abstract](690) +[HTML](149) +[PDF](2472.3KB)
Abstract:
Nonlinear differential equations: Lie symmetries, conservation laws and other approaches of solving
Chaudry Masood Khalique, Muhammad Usman and Maria Luz Gandarais
2020, 13(10): i-ii doi: 10.3934/dcdss.2020415 +[Abstract](743) +[HTML](161) +[PDF](75.78KB)
Abstract:
From the guest editors: "Delay Differential Equations: Theory, Applications and New Trends"
Fathalla A. Rihan, Yang Kuang and Gennady Bocharov
2020, 13(9): i-iv doi: 10.3934/dcdss.2020404 +[Abstract](643) +[HTML](173) +[PDF](379.29KB)
Abstract:
Special issue dedicated to SFBT 2017
Alain Miranville
2020, 13(8): i-i doi: 10.3934/dcdss.2020179 +[Abstract](636) +[HTML](167) +[PDF](67.56KB)
Abstract:
Preface to this special issue
Genni Fragnelli, Dimitri Mugnai and Maria Cesarina Salvatori
2020, 13(7): ⅰ-ⅱ doi: 10.3934/dcdss.2020147 +[Abstract](677) +[HTML](178) +[PDF](159.7KB)
Abstract:
Preface: Advances in theory and real world applications of control and dynamic optimization
Changjun Yu, Honglei Xu and Kok Lay Teo
2020, 13(6): ⅰ-ⅲ doi: 10.3934/dcdss.2020094 +[Abstract](585) +[HTML](94) +[PDF](89.39KB)
Abstract:
Preface to this special issue
Genni Fragnelli, Luca Lorenzi and Alain Miranville
2020, 13(5): ⅰ-ⅲ doi: 10.3934/dcdss.2020080 +[Abstract](903) +[HTML](179) +[PDF](1559.81KB)
Abstract:
Preface on "New trends of numerical and analytical methods"
Abdon Atangana, José Francisco Gómez-Aguilar, Jordan Y. Hristov and Kolade M. Owolabi
2020, 13(3): ⅰ-ⅱ doi: 10.3934/dcdss.20203i +[Abstract](1308) +[HTML](147) +[PDF](75.82KB)
Abstract:
The replacement of the retracted preface
Juan L. G. Guirao and Alain Miranville
2019, 12(4&5): ⅲ-ⅳ doi: 10.3934/dcdss.2020320 +[Abstract](419) +[HTML](219) +[PDF](147.32KB)
Abstract:
Dynamical systems and geometric mechanics: A special issue in Honor of Jürgen Scheurle
Thomas Hagen, Andreas Johann, Hans-Peter Kruse, Florian Rupp and Sebastian Walcher
2020, 13(4): ⅰ-ⅲ doi: 10.3934/dcdss.20204i +[Abstract](2218) +[HTML](285) +[PDF](92.43KB)
Abstract:
Preface: Analysis of cross-diffusion systems
Michael Winkler and Dariusz Wrzosek
2020, 13(2): ⅰ-ⅰ doi: 10.3934/dcdss.20202i +[Abstract](1339) +[HTML](178) +[PDF](70.65KB)
Abstract:
Preface: Delay differential equations with state-dependent delays and their applications
Qingwen Hu, Bernhard Lani-Wayda and Eugen Stumpf
2020, 13(1): ⅰ-ⅰ doi: 10.3934/dcdss.20201i +[Abstract](1269) +[HTML](166) +[PDF](94.53KB)
Abstract:
Special issue on fractal geometry, dynamical systems, and their applications
Michael Barnsley, James Keesling and Mrinal Kanti Roychowdhury
2019, 12(8): ⅰ-ⅰ doi: 10.3934/dcdss.201908i +[Abstract](1494) +[HTML](145) +[PDF](108.2KB)
Abstract:
Preface: Special issue of DCDS-S dedicated to the 70th birthday of Norman Dancer
Zalman Balanov, Wiesław Krawcewicz and Jianshe Yu
2019, 12(7): ⅰ-ⅱ doi: 10.3934/dcdss.20197i +[Abstract](1788) +[HTML](176) +[PDF](1369.58KB)
Abstract:
Preface
Laurence Cherfils, Alain Cimetière, Aziz Hamdouni, Michel Jean and Elaine Pratt
2019, 12(6): ⅰ-ⅱ doi: 10.3934/dcdss.201906i +[Abstract](1762) +[HTML](206) +[PDF](81.11KB)
Abstract:
Generalised Lyapunov-Razumikhin techniques for scalar state-dependent delay differential equations
F. M. G. Magpantay and A. R. Humphries
2020, 13(1): 85-104 doi: 10.3934/dcdss.2020005 +[Abstract](3460) +[HTML](1171) +[PDF](10539.3KB)
Abstract:

We present generalised Lyapunov-Razumikhin techniques for establishing global asymptotic stability of steady-state solutions of scalar delay differential equations. When global asymptotic stability cannot be established, the technique can be used to derive bounds on the persistent dynamics. The method is applicable to constant and variable delay problems, and we illustrate the method by applying it to the state-dependent delay differential equation known as the sawtooth equation, to find parameter regions for which the steady-state solution is globally asymptotically stable. We also establish bounds on the periodic orbits that arise when the steady-state is unstable. This technique can be readily extended to apply to other scalar delay differential equations with negative feedback.

2019  Impact Factor: 1.233

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