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Discrete & Continuous Dynamical Systems (DCDS) publishes peer-reviewed original and expository papers on the theory, methods and applications of analysis, differential equations and dynamical systems. The journal is committed to recording important new methods and results in its field and maintains the highest standards of innovation and quality. To be published in this journal, an original paper must be correct, new, nontrivial and of interest to a substantial number of readers.


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Dynamics of particles on a curve with pairwise hyper-singular repulsion
Douglas Hardin, Edward B. Saff, Ruiwen Shu and Eitan Tadmor
2021, 41(12) : 5509-5536 doi: 10.3934/dcds.2021086 +[Abstract](492) +[HTML](223) +[PDF](711.64KB)
Hearing the shape of right triangle billiard tables
Yang Shen and Jiazhong Yang
2021, 41(12) : 5537-5549 doi: 10.3934/dcds.2021087 +[Abstract](418) +[HTML](241) +[PDF](3226.82KB)
Concentration phenomena for magnetic Kirchhoff equations with critical growth
Chao Ji and Vicenţiu D. Rădulescu
2021, 41(12) : 5551-5577 doi: 10.3934/dcds.2021088 +[Abstract](483) +[HTML](218) +[PDF](517.57KB)
Classification of transitive group actions
Kesong Yan, Qian Liu and Fanping Zeng
2021, 41(12) : 5579-5607 doi: 10.3934/dcds.2021089 +[Abstract](388) +[HTML](187) +[PDF](488.31KB)
Well-posedness of the two-phase flow problem in incompressible MHD
Changyan Li and Hui Li
2021, 41(12) : 5609-5632 doi: 10.3934/dcds.2021090 +[Abstract](429) +[HTML](173) +[PDF](507.52KB)
Period tripling and quintupling renormalizations below $ C^2 $ space
Rohit Kumar and V.V.M.S. Chandramouli
2021, 41(12) : 5633-5658 doi: 10.3934/dcds.2021091 +[Abstract](410) +[HTML](181) +[PDF](861.17KB)
The nonlinear fractional relativistic Schrödinger equation: Existence, multiplicity, decay and concentration results
Vincenzo Ambrosio
2021, 41(12) : 5659-5705 doi: 10.3934/dcds.2021092 +[Abstract](441) +[HTML](176) +[PDF](645.56KB)
Dispersive estimates for the wave and the Klein-Gordon equations in large time inside the Friedlander domain
Oana Ivanovici
2021, 41(12) : 5707-5742 doi: 10.3934/dcds.2021093 +[Abstract](379) +[HTML](164) +[PDF](614.47KB)
Extinction or coexistence in periodic Kolmogorov systems of competitive type
Isabel Coelho, Carlota Rebelo and Elisa Sovrano
2021, 41(12) : 5743-5764 doi: 10.3934/dcds.2021094 +[Abstract](393) +[HTML](177) +[PDF](394.59KB)
Grassmannian reduction of cucker-smale systems and dynamical opinion games
Daniel Lear, David N. Reynolds and Roman Shvydkoy
2021, 41(12) : 5765-5787 doi: 10.3934/dcds.2021095 +[Abstract](346) +[HTML](169) +[PDF](460.08KB)
Stabilization of nonautonomous parabolic equations by a single moving actuator
Behzad Azmi, Karl Kunisch and Sérgio S. Rodrigues
2021, 41(12) : 5789-5824 doi: 10.3934/dcds.2021096 +[Abstract](354) +[HTML](169) +[PDF](1377.62KB)
Sharp well-posedness of the Cauchy problem for the rotation-modified Kadomtsev-Petviashvili equation in anisotropic Sobolev spaces
Wei Yan, Yimin Zhang, Yongsheng Li and Jinqiao Duan
2021, 41(12) : 5825-5849 doi: 10.3934/dcds.2021097 +[Abstract](308) +[HTML](165) +[PDF](489.06KB)
Sharp critical thresholds in a hyperbolic system with relaxation
Manas Bhatnagar and Hailiang Liu
2021, 41(12) : 5851-5869 doi: 10.3934/dcds.2021098 +[Abstract](319) +[HTML](172) +[PDF](399.19KB)
Discrete spectrum for amenable group actions
Tao Yu, Guohua Zhang and Ruifeng Zhang
2021, 41(12) : 5871-5886 doi: 10.3934/dcds.2021099 +[Abstract](323) +[HTML](163) +[PDF](418.19KB)
On the number of invariant measures for random expanding maps in higher dimensions
Fawwaz Batayneh and Cecilia González-Tokman
2021, 41(12) : 5887-5914 doi: 10.3934/dcds.2021100 +[Abstract](346) +[HTML](173) +[PDF](580.28KB)
Maximal chain continuous factor
Noriaki Kawaguchi
2021, 41(12) : 5915-5942 doi: 10.3934/dcds.2021101 +[Abstract](336) +[HTML](168) +[PDF](393.08KB)
Bifurcations in asymptotically autonomous Hamiltonian systems under oscillatory perturbations
Oskar A. Sultanov
2021, 41(12) : 5943-5978 doi: 10.3934/dcds.2021102 +[Abstract](345) +[HTML](181) +[PDF](1696.49KB)
On pushed wavefronts of monostable equation with unimodal delayed reaction
Karel Hasík, Jana Kopfová, Petra Nábělková and Sergei Trofimchuk
2021, 41(12) : 5979-6000 doi: 10.3934/dcds.2021103 +[Abstract](330) +[HTML](196) +[PDF](3972.42KB)
Global wellposedness of nutrient-taxis systems derived by a food metric
Jaewook Ahn, Sun-Ho Choi and Minha Yoo
2021, 41(12) : 6001-6022 doi: 10.3934/dcds.2021104 +[Abstract](378) +[HTML](176) +[PDF](372.57KB)
Wavefronts for degenerate diffusion-convection reaction equations with sign-changing diffusivity
Diego Berti, Andrea Corli and Luisa Malaguti
2021, 41(12) : 6023-6046 doi: 10.3934/dcds.2021105 +[Abstract](372) +[HTML](167) +[PDF](404.54KB)
On the compactness threshold in the critical Kirchhoff equation
Erisa Hasani and Kanishka Perera
2021doi: 10.3934/dcds.2021106 +[Abstract](584) +[HTML](177) +[PDF](501.7KB)
On the number of positive solutions to an indefinite parameter-dependent Neumann problem
Guglielmo Feltrin, Elisa Sovrano and Andrea Tellini
2021doi: 10.3934/dcds.2021107 +[Abstract](316) +[HTML](153) +[PDF](871.3KB)
Upper semicontinuity of pullback attractors for non-autonomous lattice systems under singular perturbations
Na Lei and Shengfan Zhou
2021doi: 10.3934/dcds.2021108 +[Abstract](269) +[HTML](117) +[PDF](609.76KB)
Global existence of solutions to reaction diffusion systems with mass transport type boundary conditions on an evolving domain
Vandana Sharma and Jyotshana V. Prajapat
2021doi: 10.3934/dcds.2021109 +[Abstract](12) +[HTML](14) +[PDF](509.31KB)
A semilinear problem with a gradient term in the nonlinearity
Ignacio Guerra
2021doi: 10.3934/dcds.2021110 +[Abstract](239) +[HTML](119) +[PDF](334.75KB)
Combined effects of singular and exponential nonlinearities in fractional Kirchhoff problems
Tuhina Mukherjee, Patrizia Pucci and Mingqi Xiang
2021doi: 10.3934/dcds.2021111 +[Abstract](271) +[HTML](138) +[PDF](526.22KB)
Orbit counting in polarized dynamical systems
Wade Hindes
2021doi: 10.3934/dcds.2021112 +[Abstract](185) +[HTML](115) +[PDF](584.26KB)
The relaxation limit of bipolar fluid models
Nuno J. Alves and Athanasios E. Tzavaras
2021doi: 10.3934/dcds.2021113 +[Abstract](206) +[HTML](98) +[PDF](447.84KB)
Families of vector fields with many numerical invariants
Nataliya Goncharuk and Yury Kudryashov
2021doi: 10.3934/dcds.2021114 +[Abstract](186) +[HTML](118) +[PDF](510.08KB)
On a curvature flow in a band domain with unbounded boundary slopes
Lixia Yuan and Wei Zhao
2021doi: 10.3934/dcds.2021115 +[Abstract](174) +[HTML](106) +[PDF](618.91KB)
Shadowing for families of endomorphisms of generalized group shifts
Xuan Kien Phung
2021doi: 10.3934/dcds.2021116 +[Abstract](193) +[HTML](96) +[PDF](418.49KB)
Estimates the upper bounds of Dirichlet eigenvalues for fractional Laplacian
Hua Chen and Hong-Ge Chen
2021doi: 10.3934/dcds.2021117 +[Abstract](195) +[HTML](108) +[PDF](500.23KB)
Subhyperbolic rational maps on boundaries of hyperbolic components
Yan Gao, Luxian Yang and Jinsong Zeng
2021doi: 10.3934/dcds.2021118 +[Abstract](172) +[HTML](87) +[PDF](331.42KB)
The geodesic flow on nilpotent Lie groups of steps two and three
Gabriela P. Ovando
2021doi: 10.3934/dcds.2021119 +[Abstract](178) +[HTML](93) +[PDF](530.75KB)
Inducing schemes for multi-dimensional piecewise expanding maps
Peyman Eslami
2021doi: 10.3934/dcds.2021120 +[Abstract](179) +[HTML](96) +[PDF](483.38KB)
Decay estimates for Schrödinger heat semigroup with inverse square potential in Lorentz spaces II
Kazuhiro Ishige and Yujiro Tateishi
2021doi: 10.3934/dcds.2021121 +[Abstract](200) +[HTML](82) +[PDF](651.86KB)
The critical points of the elastic energy among curves pinned at endpoints
Kensuke Yoshizawa
2021doi: 10.3934/dcds.2021122 +[Abstract](179) +[HTML](89) +[PDF](1431.6KB)
The Brinkman-Fourier system with ideal gas equilibrium
Chun Liu and Jan-Eric Sulzbach
2021doi: 10.3934/dcds.2021123 +[Abstract](248) +[HTML](91) +[PDF](515.34KB)
Exact null-controllability of interconnected abstract evolution equations with unbounded input operators
Benzion Shklyar
2021doi: 10.3934/dcds.2021124 +[Abstract](177) +[HTML](89) +[PDF](302.35KB)
A log–exp elliptic equation in the plane
Giovany Figueiredo, Marcelo Montenegro and Matheus F. Stapenhorst
2021doi: 10.3934/dcds.2021125 +[Abstract](230) +[HTML](89) +[PDF](407.79KB)
Exact description of SIR-Bass epidemics on 1D lattices
Gadi Fibich and Samuel Nordmann
2021doi: 10.3934/dcds.2021126 +[Abstract](173) +[HTML](96) +[PDF](460.53KB)
$ W^{1, p} $ estimates for elliptic problems with drift terms in Lipschitz domains
Bojing Shi
2021doi: 10.3934/dcds.2021127 +[Abstract](193) +[HTML](93) +[PDF](362.92KB)
Aubry-Mather theory for contact Hamiltonian systems II
Kaizhi Wang, Lin Wang and Jun Yan
2021doi: 10.3934/dcds.2021128 +[Abstract](150) +[HTML](95) +[PDF](588.98KB)
Realizing arbitrary $d$-dimensional dynamics by renormalization of $C^d$-perturbations of identity
Bassam Fayad and Maria Saprykina
2021doi: 10.3934/dcds.2021129 +[Abstract](140) +[HTML](74) +[PDF](178.97KB)
Propagating fronts for a viscous Hamer-type system
Giada Cianfarani Carnevale, Corrado Lattanzio and Corrado Mascia
2021doi: 10.3934/dcds.2021130 +[Abstract](138) +[HTML](70) +[PDF](427.65KB)
Forward triplets and topological entropy on trees
Lluís Alsedà, David Juher and Francesc Mañosas
2021doi: 10.3934/dcds.2021131 +[Abstract](159) +[HTML](85) +[PDF](481.04KB)
Pullback attractors for 2D MHD equations on time-varying domains
Daomin Cao, Xiaoya Song and Chunyou Sun
2021doi: 10.3934/dcds.2021132 +[Abstract](151) +[HTML](66) +[PDF](571.28KB)
On the fractional susceptibility function of piecewise expanding maps
Magnus Aspenberg, Viviane Baladi, Juho Leppänen and Tomas Persson
2021doi: 10.3934/dcds.2021133 +[Abstract](140) +[HTML](68) +[PDF](284.65KB)
Generalization of the Winfree model to the high-dimensional sphere and its emergent dynamics
Hansol Park
2021doi: 10.3934/dcds.2021134 +[Abstract](133) +[HTML](69) +[PDF](561.5KB)
Stabilization of periodic sweeping processes and asymptotic average velocity for soft locomotors with dry friction
Giovanni Colombo, Paolo Gidoni and Emilio Vilches
2021doi: 10.3934/dcds.2021135 +[Abstract](160) +[HTML](68) +[PDF](536.48KB)
Global existence and convergence to steady states for a predator-prey model with both predator- and prey-taxis
Guoqiang Ren and Bin Liu
2021doi: 10.3934/dcds.2021136 +[Abstract](150) +[HTML](95) +[PDF](511.96KB)
Singular weighted sharp Trudinger-Moser inequalities defined on $ \mathbb{R}^N $ and applications to elliptic nonlinear equations
Sami Aouaoui and Rahma Jlel
2021doi: 10.3934/dcds.2021137 +[Abstract](144) +[HTML](76) +[PDF](613.85KB)
Quantitative statistical stability and linear response for irrational rotations and diffeomorphisms of the circle
Stefano Galatolo and Alfonso Sorrentino
2021doi: 10.3934/dcds.2021138 +[Abstract](135) +[HTML](65) +[PDF](589.44KB)
Cohomology groups, continuous full groups and continuous orbit equivalence of topological Markov shifts
Kengo Matsumoto
2021doi: 10.3934/dcds.2021139 +[Abstract](123) +[HTML](66) +[PDF](352.01KB)
Pure strictly uniform models of non-ergodic measure automorphisms
Tomasz Downarowicz and Benjamin Weiss
2021doi: 10.3934/dcds.2021140 +[Abstract](127) +[HTML](64) +[PDF](1588.76KB)
Global stability solution of the 2D MHD equations with mixed partial dissipation
Yana Guo, Yan Jia and Bo-Qing Dong
2021doi: 10.3934/dcds.2021141 +[Abstract](158) +[HTML](72) +[PDF](307.3KB)
The nonlocal-interaction equation near attracting manifolds
Francesco S. Patacchini and Dejan Slepčev
2021doi: 10.3934/dcds.2021142 +[Abstract](124) +[HTML](66) +[PDF](565.89KB)
Characterizing entropy dimensions of minimal mutidimensional subshifts of finite type
Silvère Gangloff
2021doi: 10.3934/dcds.2021143 +[Abstract](54) +[HTML](28) +[PDF](837.74KB)
Criniferous entire maps with absorbing Cantor bouquets
Leticia Pardo-Simón
2021doi: 10.3934/dcds.2021144 +[Abstract](44) +[HTML](18) +[PDF](736.75KB)
On the improved interior regularity of a boundary value problem modelling the displacement of a linearly elastic elliptic membrane shell subject to an obstacle
Paolo Piersanti
2021doi: 10.3934/dcds.2021145 +[Abstract](50) +[HTML](27) +[PDF](662.54KB)
Periodic and asymptotically periodic fourth-order Schrödinger equations with critical and subcritical growth
Edcarlos D. Silva, Marcos L. M. Carvalho and Claudiney Goulart
2021doi: 10.3934/dcds.2021146 +[Abstract](56) +[HTML](21) +[PDF](572.29KB)
Local well-posedness for the Zakharov system in dimension d ≤ 3
Akansha Sanwal
2021doi: 10.3934/dcds.2021147 +[Abstract](73) +[HTML](25) +[PDF](685.52KB)
Zero-dimensional and symbolic extensions of topological flows
David Burguet and Ruxi Shi
2021doi: 10.3934/dcds.2021148 +[Abstract](54) +[HTML](23) +[PDF](591.74KB)
Two species nonlocal diffusion systems with free boundaries
Yihong Du, Mingxin Wang and Meng Zhao
2021doi: 10.3934/dcds.2021149 +[Abstract](142) +[HTML](61) +[PDF](601.05KB)
Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
Jie Shen and Xiaofeng Yang
2010, 28(4) : 1669-1691 doi: 10.3934/dcds.2010.28.1669 +[Abstract](8570) +[PDF](382.7KB) Cited By(319)
Variational methods for non-local operators of elliptic type
Raffaella Servadei and Enrico Valdinoci
2013, 33(5) : 2105-2137 doi: 10.3934/dcds.2013.33.2105 +[Abstract](5726) +[PDF](418.8KB) Cited By(292)
Global well-posedness of the viscous Boussinesq equations
Thomas Y. Hou and Congming Li
2005, 12(1) : 1-12 doi: 10.3934/dcds.2005.12.1 +[Abstract](4301) +[PDF](203.5KB) Cited By(209)
Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation
Xiaoyue Li and Xuerong Mao
2009, 24(2) : 523-545 doi: 10.3934/dcds.2009.24.523 +[Abstract](7906) +[PDF](262.8KB) Cited By(202)
Well-posedness and blow-up phenomena for the 2-component Camassa-Holm equation
Joachim Escher, Olaf Lechtenfeld and Zhaoyang Yin
2007, 19(3) : 493-513 doi: 10.3934/dcds.2007.19.493 +[Abstract](5711) +[PDF](233.8KB) Cited By(202)
Global attractors for damped semilinear wave equations
John M. Ball
2004, 10(1&2) : 31-52 doi: 10.3934/dcds.2004.10.31 +[Abstract](7079) +[PDF](246.2KB) Cited By(198)
Partial regularity of the dynamic system modeling the flow of liquid crystals
Fanghua Lin and Chun Liu
1996, 2(1) : 1-22 doi: 10.3934/dcds.1996.2.1 +[Abstract](3897) +[PDF](222.9KB) Cited By(170)
The problem Of blow-up in nonlinear parabolic equations
Victor A. Galaktionov and Juan-Luis Vázquez
2002, 8(2) : 399-433 doi: 10.3934/dcds.2002.8.399 +[Abstract](6339) +[PDF](369.4KB) Cited By(169)
Remarks on regularities for the 3D MHD equations
Yong Zhou
2005, 12(5) : 881-886 doi: 10.3934/dcds.2005.12.881 +[Abstract](4582) +[PDF](176.3KB) Cited By(168)
Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model
Linda J. S. Allen, B. M. Bolker, Yuan Lou and A. L. Nevai
2008, 21(1) : 1-20 doi: 10.3934/dcds.2008.21.1 +[Abstract](8085) +[PDF](401.1KB) Cited By(155)
The problem Of blow-up in nonlinear parabolic equations
Victor A. Galaktionov and Juan-Luis Vázquez
2002, 8(2) : 399-433 doi: 10.3934/dcds.2002.8.399 +[Abstract](6339) +[PDF](369.4KB) PDF Downloads(1945)
Some questions looking for answers in dynamical systems
Carles Simó
2018, 38(12) : 6215-6239 doi: 10.3934/dcds.2018267 +[Abstract](5694) +[HTML](367) +[PDF](531.03KB) PDF Downloads(1769)
The vorticity equation on a rotating sphere and the shallow fluid approximation
Vikas S. Krishnamurthy
2019, 39(11) : 6261-6276 doi: 10.3934/dcds.2019273 +[Abstract](1851) +[HTML](166) +[PDF](370.02KB) PDF Downloads(1311)
Conditional measures and conditional expectation; Rohlin's Disintegration Theorem
David Simmons
2012, 32(7) : 2565-2582 doi: 10.3934/dcds.2012.32.2565 +[Abstract](3696) +[PDF](444.9KB) PDF Downloads(1122)
Differentiability of the Hartman--Grobman linearization
Misha Guysinsky, Boris Hasselblatt and Victoria Rayskin
2003, 9(4) : 979-984 doi: 10.3934/dcds.2003.9.979 +[Abstract](2795) +[PDF](131.0KB) PDF Downloads(946)
Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
Jie Shen and Xiaofeng Yang
2010, 28(4) : 1669-1691 doi: 10.3934/dcds.2010.28.1669 +[Abstract](8570) +[PDF](382.7KB) PDF Downloads(782)
Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model
Linda J. S. Allen, B. M. Bolker, Yuan Lou and A. L. Nevai
2008, 21(1) : 1-20 doi: 10.3934/dcds.2008.21.1 +[Abstract](8085) +[PDF](401.1KB) PDF Downloads(754)
On the spectral theory of positive operators and PDE applications
Kung-Ching Chang, Xuefeng Wang and Xie Wu
2020, 40(6) : 3171-3200 doi: 10.3934/dcds.2020054 +[Abstract](2241) +[HTML](667) +[PDF](460.48KB) PDF Downloads(675)
On Geometric Mechanics
Jean-Marie Souriau
2007, 19(3) : 595-607 doi: 10.3934/dcds.2007.19.595 +[Abstract](2467) +[PDF](183.4KB) PDF Downloads(611)
Regularity and classification of solutions to static Hartree equations involving fractional Laplacians
Wei Dai, Jiahui Huang, Yu Qin, Bo Wang and Yanqin Fang
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2020 Impact Factor: 1.392
5 Year Impact Factor: 1.610
2020 CiteScore: 2.2

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