Citation: Cristeta U. Jamilla, Renier G. Mendoza, Victoria May P. Mendoza. Explicit solution of a Lotka-Sharpe-McKendrick system involving neutral delay differential equations using the r-Lambert W function[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 5686-5708. doi: 10.3934/mbe.2020306
[1] | F. M. Asl, G. A. Ulsoy, Analysis of a system of linear delay differential equations, ASME J. Dyn. Sys., Meas., Control, 125 (2003), 215-223. |
[2] | S. Yi, P. W. Nelson, A. G. Ulsoy, Solution of systems of linear delay differential equations via Laplace transformation, in Proceedings of the 45th IEEE Conference on Decision and Control, IEEE, (2006), 2535-2540. |
[3] | S. Yi, P. W. Nelson, A. G. Ulsoy, Survey on analysis of time delayed systems via the Lambert W function, Differ. Equations, 14 (2007), 296-301. |
[4] | S. Yi, A. G. Ulsoy, Solution of a system of linear delay differential equations using the matrix Lambert function, in Proceedings of 2006 American Control Conference, Minneapolis, IEEE, (2006), 2433-2438. |
[5] | R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, D. E. Knuth, On the Lambert w function, Adv. Comput. Math., 5 (1996), 329-359. |
[6] | I. Mezö, G. Keady, Some physical applications of generalized Lambert functions, Eur. J. Phys., 37 (2016), 065802. |
[7] | I. Mezö, A. Baricz, On the generalization of the lambert W function, Trans. Amer. Math. Soc., 369 (2017), 7917-7934. |
[8] | I. Mezö, On the structure of the solution set of a generalized Euler-Lambert equation, J. Math. Anal. Appl., 455, (2017), 538-553. |
[9] | C. B. Corcino, R. B. Corcino, An asymptotic formula for r-Bell numbers with real arguments, ISRN Discrete Math., 2013 (2013). |
[10] | V. Barsan, Inverses of Langevin, Brillouin and related functions: a status report, Rom. Rep. Phys., 72 (2020). |
[11] | C. Ewerhart, G. Z. Sun, Equilibrium in the symmetric two-player Hirshleifer contest: uniqueness and characterization, Econ. Lett., 169 (2018), 51-54. |
[12] | L. M. Briceño-Arias, G. Chierchia, E. Chouzenoux, J. C. Pesquet, A random block-coordinate Douglas-Rachford splitting method with low computational complexity for binary logistic regression, Comput. Optim. Appl., 72 (2019), 707-726. |
[13] | V. Barsan, Simple and accurate approximants of inverse Brillouin functions, J. Magn. Magn. Mater., 473 (2019), 399-402. |
[14] | V. Barsan, Siewert solutions of transcendental equations, generalized Lambert functions and physical applications, Open Phys., 16 (2018), 232-242. |
[15] | V. Barsan, New results concerning the generalized Lambert functions and their applications to solar energy conversion and nanophysics, CTP-Trieste, Spectroscopy and Dynamics of Photoinduced Electronic Excitations (Workshop Poster), 2017. Available from: https://www.researchgate.net. |
[16] | D. Belkić, All the trinomial roots, their powers and logarithms from the Lambert series, Bell polynomials and fox-wright function: illustration for genome multiplicity in survival of irradiated cells, J. Math. Chem., 57 (2019), 59-106. |
[17] | N. Bovenzi, Spin-momentum locking in oxide interfaces and in Weyl semimetals, Ph.D. thesis, University of Leiden, 2018. |
[18] | N. Bovenzi, M. Breitkreiz, T. E. O'Brien, J. Tworzydło, C. W. J. Beenakker, Twisted fermi surface of a thin-film Weyl semimetal, New J. Phys., 20 (2018), 023023. |
[19] | R. M. Digilov, Gravity discharge vessel revisited: an explicit Lambert W function solution, Am. J. Phys., 85 (2017) 510-514. |
[20] | J. Guo, Exact procedure for Einstein-Johnson's sidewall correction in open channel flow, J. Hydraul. Eng., 143 (2017), 06016027. |
[21] | R. Jedynak, A comprehensive study of the mathematical methods used to approximate the inverse Langevin function, Math. Mech. Solids., 24 (2019), 1992-2016. |
[22] | R. Jedynak, New facts concerning the approximation of the inverse Langevin function, J. Nonnewton Fluid Mech., 249 (2017), 8-25. |
[23] | I. Lopez-Garcia, C. S. Lopez-Monsalvo, E. Campero-Littlewood, F. Beltran-Carbajal, E. Campero-Littlewood, Alternative modes of operation for wind energy conversion systems and the generalised Lambert W-function, IET Gener. Transm. Distrib., 12 (2018), 3152-3157. |
[24] | B. C. Marchi, E. M. Arruda, Generalized error-minimizing, rational inverse Langevin approximations, Math. Mech. Solids., 24 (2019), 1630-1647. |
[25] | O. Olendski, Thermodynamic properties of the 1D Robin quantum well, Ann. Phys., 530 (2018). |
[26] | S. Rebollo-Perdomo, C. Vidal, Bifurcation of limit cycles for a family of perturbed Kukles differential systems, Am. Inst. Math. Sci. Discrete Contin. Dyn. Syst. A, 38 (2018), 4189-4202. |
[27] | H. Vazquez-Leal, M. A. Sandoval-Hernandez, J. L. Garcia-Gervacio, A. L. Herrera-May, U. A. Filobello-Nino, PSEM approximations for both branches of Lambert W function with applications, Discrete Dyn. Nat. Soc., 2019 (2019). |
[28] | M. Vono, P. Chainais, Sparse Bayesian binary logistic regression using the split-and-augmented Gibbs sampler, in Proceedings of 2018 IEEE International Workshop on Machine Learning for Signal Processing, IEEE, (2018). |
[29] | C. Jamilla, R. Mendoza, I. Mezö, Solutions of neutral delay differential equations using a generalized Lambert W function, Appl. Math. Comput., 382 (2020), 125334. |
[30] | G. Bocharov, K. P. Hadeler, Structured population models, conservation Laws, and delay equations, J. Differ. Equations, 168 (2000), 212-237. |
[31] | P. J. Gullan, P. S. Cranston, The Insects: An Outline of Entomology, 5^{th} edition, John Wiley & Sons, Ltd, 2014. |
[32] | M. A. Zabek, Understanding population dynamics of feral horses in the Tuan and Toolara State Forest for successful long-term population management, Ph.D. thesis, The University of Queensland, 2015. |
[33] | M. A. Zabek, D. M. Berman, S. P. Blomberg, C. W. Collins, J. Wright, Population dynamics of feral horses (Equus caballus) in an exotic coniferous plantation in Australia, Wildlife Res., 43 (2016), 358-367. |
[34] | S. A. Gourley, Y. Kuang, Dynamics of a neutral delay equation for an insect population with long larval and short adult phases, J. Differ. Equations, 246 (2009), 4653-4669. |
[35] | K. S. Williams, C. Simon, The ecology, behavior and evolution of periodical cicadas, Annu. Rev. Entomol., 40 (1995), 269-295. |
[36] | K. Soong, G. F. Chen, J. R. Cao, Life history studies of the flightless marine midges Pontomyia spp. (Diptera: Chironomidae), Zool. Stud., 38 (1999), 466-473. |
[37] | J. E. Brittain, M. Sartori, Ephemeroptera:(Mayflies), in Encyclopedia of Insects, Academic Press, (2009), 33-75. |
[38] | B. Dorociaková, I. Ilavská, R. Olach, Existence of solutions for an age-structured insect population model with a larval stage, Electron. J. Qual. Theo., 65 (2017), 1-14. |