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A gradient flow scheme for nonlinear fourth order equations
Period increment cascades in a discontinuous map with squareroot singularity
1.  Department of Mathematics and Centre for Theoretical Studies, Indian Institute of Technology, Kharagpur721302, West Bengal, India 
2.  Department of Physical Sciences, Indian Institute of Science Education and Research, Mohanpur741252, Nadia, West Bengal, India 
[1] 
Laura Gardini, Roya Makrooni, Iryna Sushko. Cascades of alternating smooth bifurcations and border collision bifurcations with singularity in a family of discontinuous linearpower maps. Discrete and Continuous Dynamical Systems  B, 2018, 23 (2) : 701729. doi: 10.3934/dcdsb.2018039 
[2] 
Hun Ki Baek, Younghae Do. Dangerous BorderCollision bifurcations of a piecewisesmooth map. Communications on Pure and Applied Analysis, 2006, 5 (3) : 493503. doi: 10.3934/cpaa.2006.5.493 
[3] 
Zhiying Qin, Jichen Yang, Soumitro Banerjee, Guirong Jiang. Bordercollision bifurcations in a generalized piecewise linearpower map. Discrete and Continuous Dynamical Systems  B, 2011, 16 (2) : 547567. doi: 10.3934/dcdsb.2011.16.547 
[4] 
Iryna Sushko, Anna Agliari, Laura Gardini. Bistability and bordercollision bifurcations for a family of unimodal piecewise smooth maps. Discrete and Continuous Dynamical Systems  B, 2005, 5 (3) : 881897. doi: 10.3934/dcdsb.2005.5.881 
[5] 
Vincenzo Ambrosio, Giovanni Molica Bisci, Dušan Repovš. Nonlinear equations involving the square root of the Laplacian. Discrete and Continuous Dynamical Systems  S, 2019, 12 (2) : 151170. doi: 10.3934/dcdss.2019011 
[6] 
Theresa Lange, Wilhelm Stannat. Mean field limit of Ensemble Square Root filters  discrete and continuous time. Foundations of Data Science, 2021, 3 (3) : 563588. doi: 10.3934/fods.2021003 
[7] 
Christian Wolf. A shift map with a discontinuous entropy function. Discrete and Continuous Dynamical Systems, 2020, 40 (1) : 319329. doi: 10.3934/dcds.2020012 
[8] 
GianItalo Bischi, Laura Gardini, Fabio Tramontana. Bifurcation curves in discontinuous maps. Discrete and Continuous Dynamical Systems  B, 2010, 13 (2) : 249267. doi: 10.3934/dcdsb.2010.13.249 
[9] 
James W. Cannon, Mark H. Meilstrup, Andreas Zastrow. The period set of a map from the Cantor set to itself. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 26672679. doi: 10.3934/dcds.2013.33.2667 
[10] 
Thai Son Doan, Martin Rasmussen, Peter E. Kloeden. The meansquare dichotomy spectrum and a bifurcation to a meansquare attractor. Discrete and Continuous Dynamical Systems  B, 2015, 20 (3) : 875887. doi: 10.3934/dcdsb.2015.20.875 
[11] 
Àngel Jorba, Pau Rabassa, Joan Carles Tatjer. Period doubling and reducibility in the quasiperiodically forced logistic map. Discrete and Continuous Dynamical Systems  B, 2012, 17 (5) : 15071535. doi: 10.3934/dcdsb.2012.17.1507 
[12] 
ChanGyun Kim, YongHoon Lee. A bifurcation result for two point boundary value problem with a strong singularity. Conference Publications, 2011, 2011 (Special) : 834843. doi: 10.3934/proc.2011.2011.834 
[13] 
Meihua Wei, Yanling Li, Xi Wei. Stability and bifurcation with singularity for a glycolysis model under noflux boundary condition. Discrete and Continuous Dynamical Systems  B, 2019, 24 (9) : 52035224. doi: 10.3934/dcdsb.2019129 
[14] 
Jianfeng Huang, Yulin Zhao. Bifurcation of isolated closed orbits from degenerated singularity in $\mathbb{R}^{3}$. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 28612883. doi: 10.3934/dcds.2013.33.2861 
[15] 
Jianfei Cheng, Xiao Wang, Yicheng Liu. Collisionavoidance and flocking in the Cucker–Smaletype model with a discontinuous controller. Discrete and Continuous Dynamical Systems  S, 2022, 15 (7) : 17331748. doi: 10.3934/dcdss.2021169 
[16] 
Yuncherl Choi, Jongmin Han, ChunHsiung Hsia. Bifurcation analysis of the damped KuramotoSivashinsky equation with respect to the period. Discrete and Continuous Dynamical Systems  B, 2015, 20 (7) : 19331957. doi: 10.3934/dcdsb.2015.20.1933 
[17] 
Na An, Chaobao Huang, Xijun Yu. Error analysis of discontinuous Galerkin method for the time fractional KdV equation with weak singularity solution. Discrete and Continuous Dynamical Systems  B, 2020, 25 (1) : 321334. doi: 10.3934/dcdsb.2019185 
[18] 
Ming Zhao, Cuiping Li, Jinliang Wang, Zhaosheng Feng. Bifurcation analysis of the threedimensional Hénon map. Discrete and Continuous Dynamical Systems  S, 2017, 10 (3) : 625645. doi: 10.3934/dcdss.2017031 
[19] 
Denis Gaidashev, Tomas Johnson. Dynamics of the universal areapreserving map associated with perioddoubling: Stable sets. Journal of Modern Dynamics, 2009, 3 (4) : 555587. doi: 10.3934/jmd.2009.3.555 
[20] 
Valeria Banica, Luis Vega. Singularity formation for the 1D cubic NLS and the Schrödinger map on $\mathbb S^2$. Communications on Pure and Applied Analysis, 2018, 17 (4) : 13171329. doi: 10.3934/cpaa.2018064 
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