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Characterization of the dynamic behavior of nonlinear biosystems in the presence of model uncertainty using singular invariance PDEs: Application to immobilized enzyme and cell bioreactors
Wave fronts in neuronal fields with nonlocal postsynaptic axonal connections and delayed nonlocal feedback connections
1.  Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada 
2.  Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5B7 
[1] 
Kyudong Choi. Persistence of Hölder continuity for nonlocal integrodifferential equations. Discrete & Continuous Dynamical Systems  A, 2013, 33 (5) : 17411771. doi: 10.3934/dcds.2013.33.1741 
[2] 
YongKui Chang, Xiaojing Liu. Timevarying integrodifferential inclusions with Clarke subdifferential and nonlocal initial conditions: existence and approximate controllability. Evolution Equations & Control Theory, 2020, 9 (3) : 845863. doi: 10.3934/eect.2020036 
[3] 
Narcisa Apreutesei, Nikolai Bessonov, Vitaly Volpert, Vitali Vougalter. Spatial structures and generalized travelling waves for an integrodifferential equation. Discrete & Continuous Dynamical Systems  B, 2010, 13 (3) : 537557. doi: 10.3934/dcdsb.2010.13.537 
[4] 
Narcisa Apreutesei, Arnaud Ducrot, Vitaly Volpert. Travelling waves for integrodifferential equations in population dynamics. Discrete & Continuous Dynamical Systems  B, 2009, 11 (3) : 541561. doi: 10.3934/dcdsb.2009.11.541 
[5] 
Zhaoquan Xu, Jiying Ma. Monotonicity, asymptotics and uniqueness of travelling wave solution of a nonlocal delayed lattice dynamical system. Discrete & Continuous Dynamical Systems  A, 2015, 35 (10) : 51075131. doi: 10.3934/dcds.2015.35.5107 
[6] 
Ábel Garab. Unique periodic orbits of a delay differential equation with piecewise linear feedback function. Discrete & Continuous Dynamical Systems  A, 2013, 33 (6) : 23692387. doi: 10.3934/dcds.2013.33.2369 
[7] 
Tao Wang. Global dynamics of a nonlocal delayed differential equation in the half plane. Communications on Pure & Applied Analysis, 2014, 13 (6) : 24752492. doi: 10.3934/cpaa.2014.13.2475 
[8] 
Zhaoquan Xu, Chufen Wu. Spreading speeds for a class of nonlocal convolution differential equation. Discrete & Continuous Dynamical Systems  B, 2020 doi: 10.3934/dcdsb.2020108 
[9] 
Liang Zhang, Bingtuan Li. Traveling wave solutions in an integrodifferential competition model. Discrete & Continuous Dynamical Systems  B, 2012, 17 (1) : 417428. doi: 10.3934/dcdsb.2012.17.417 
[10] 
Tomás Caraballo, P.E. Kloeden. Nonautonomous attractors for integrodifferential evolution equations. Discrete & Continuous Dynamical Systems  S, 2009, 2 (1) : 1736. doi: 10.3934/dcdss.2009.2.17 
[11] 
Linghai Zhang. Wave speed analysis of traveling wave fronts in delayed synaptically coupled neuronal networks. Discrete & Continuous Dynamical Systems  A, 2014, 34 (5) : 24052450. doi: 10.3934/dcds.2014.34.2405 
[12] 
Walter Allegretto, John R. Cannon, Yanping Lin. A parabolic integrodifferential equation arising from thermoelastic contact. Discrete & Continuous Dynamical Systems  A, 1997, 3 (2) : 217234. doi: 10.3934/dcds.1997.3.217 
[13] 
Shihchung Chiang. Numerical optimal unbounded control with a singular integrodifferential equation as a constraint. Conference Publications, 2013, 2013 (special) : 129137. doi: 10.3934/proc.2013.2013.129 
[14] 
Frederic Abergel, Remi Tachet. A nonlinear partial integrodifferential equation from mathematical finance. Discrete & Continuous Dynamical Systems  A, 2010, 27 (3) : 907917. doi: 10.3934/dcds.2010.27.907 
[15] 
Samir K. Bhowmik, Dugald B. Duncan, Michael Grinfeld, Gabriel J. Lord. Finite to infinite steady state solutions, bifurcations of an integrodifferential equation. Discrete & Continuous Dynamical Systems  B, 2011, 16 (1) : 5771. doi: 10.3934/dcdsb.2011.16.57 
[16] 
Michel Chipot, Senoussi Guesmia. On a class of integrodifferential problems. Communications on Pure & Applied Analysis, 2010, 9 (5) : 12491262. doi: 10.3934/cpaa.2010.9.1249 
[17] 
Saulo R.M. Barros, Antônio L. Pereira, Cláudio Possani, Adilson Simonis. Spatially periodic equilibria for a non local evolution equation. Discrete & Continuous Dynamical Systems  A, 2003, 9 (4) : 937948. doi: 10.3934/dcds.2003.9.937 
[18] 
Olivier Bonnefon, Jérôme Coville, Guillaume Legendre. Concentration phenomenon in some nonlocal equation. Discrete & Continuous Dynamical Systems  B, 2017, 22 (3) : 763781. doi: 10.3934/dcdsb.2017037 
[19] 
Kaïs Ammari, Thomas Duyckaerts, Armen Shirikyan. Local feedback stabilisation to a nonstationary solution for a damped nonlinear wave equation. Mathematical Control & Related Fields, 2016, 6 (1) : 125. doi: 10.3934/mcrf.2016.6.1 
[20] 
V. Vijayakumar, R. Udhayakumar, K. Kavitha. On the approximate controllability of neutral integrodifferential inclusions of Sobolevtype with infinite delay. Evolution Equations & Control Theory, 2020 doi: 10.3934/eect.2020066 
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