Davidson Group Mathematics

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Publications

Untitled report
A report made in Pure. Prepared by: Fordyce A. Davidson (f.a.davidson@dundee.ac.uk), 12/02/15 18:25

1. Research output

Listing of Research output
Ordered by: Publication year

1.1. 2014

Davidson, FA & Savory, AIM 2014, 'Existence and meta-stability of steady states of a model for chemotaxis' Nonlinear Analysis: Real World Applications, vol 17, pp. 101-113., 10.1016/j.nonrwa.2013.10.009

Savory, AIM, Grenville-Briggs, LJ, Wawra, S, van West, P & Davidson, FA 2014, 'Auto-aggregation in zoospores of Phytophthora infestans: the cooperative roles of bioconvection and chemotaxis' Journal of the Royal Society Interface, vol 11, no. 94, 20140017., 10.1098/rsif.2014.0017

Stephenson, KS, Gow, NAR, Davidson, FA & Gadd, GM 2014, 'Regulation of vectorial supply of vesicles to the hyphal tip determines thigmotropism in Neurospora crassa' Fungal Biology, vol 118, no. 3, pp. 287-294., 10.1016/j.funbio.2013.12.007

Marlow, VL, Porter, M, Hobley, L, Kiley, TB, Swedlow, JR, Davidson, FA & Stanley-Wall, NR 2014, 'Phosphorylated DegU manipulates cell fate differentiation in the Bacillus subtilis biofilm' Journal of Bacteriology, vol 196, no. 1, pp. 16-27., 10.1128/JB.00930-13

1.2. 2013

Sargent, F, Davidson, FA, Kelly, CL, Binny, R, Christodoulides, N, Gibson, D, Johansson, E, Kozyrska, K, Licandro Lado, L, MacCallum, J, Montague, R, Ortmann, B, Owen, R, Coulthurst, SJ, Dupuy, L, Prescott, AR & Palmer, T 2013, 'A synthetic system for expression of components of a bacterial microcompartment' Microbiology-SGM, vol 159, no. 11, pp. 2427-2436., 10.1099/mic.0.069922-0

Jaffar, MZAM & Davidson, FA 2013, 'Basic rules for polarised cell growth' Journal of Theoretical Biology, vol 336, pp. 44-51., 10.1016/j.jtbi.2013.06.039

1.3. 2012

Alzahrani, EO, Davidson, FA & Dodds, N 2012, 'Reversing invasion in bistable systems' Journal of Mathematical Biology, vol 65, no. 6-7, pp. 1101-1124., 10.1007/s00285-011-0490-9

Davidson, FA, Yi, C-S & Stanley-Wall, NR 2012, 'Selective Heterogeneity in Exoprotease Production by Bacillus subtilis' PLoS ONE, vol 7, no. 6, e38574, pp. -., 10.1371/journal.pone.0038574

Alzahrani, EO, Davidson, FA & Dodds, N 2012, 'A 3-species competition model for bio-control' Applied Mathematics and Computation, vol 218, no. 19, pp. 9690-9698., 10.1016/j.amc.2012.03.012

Boswell, GP & Davidson, FA 2012, 'Modelling hyphal networks' Fungal Biology Reviews, vol 26, no. 1, pp. 30-38., 10.1016/j.fbr.2012.02.002

Davidson, FA 2012, 'Is cell fusion driven by excitation?: Comment on DOI: 10.1002/bies.201100135' BioEssays, vol 34, no. 4, pp. 258-258., 10.1002/bies.201200011

1.4. 2011

Champneys, A & Davidson, F 2011, 'Special Issue: 2020 visions of applied mathematics' IMA Journal of Applied Mathematics, vol 76, no. 3, pp. 351-352., 10.1093/imamat/hxr026

1.5. 2010

Kamei, H, Jackson, RC, Zheleva, D & Davidson, FA 2010, 'An integrated pharmacokinetic-pharmacodynamic model for an Aurora kinase inhibitor' Journal of Pharmacokinetics and Pharmacodynamics, vol 37, no. 4, pp. 407-434., 10.1007/s10928-010-9166-0

Davidson, F 2010, 'A blueprint for polarised growth' Microbiology Today, no. 34, pp. 34-37.

Mistry, HB, MacCallum, DE, Jackson, RC, Chaplain, MAJ & Davidson, FA 2010, 'A pharmacodynamic model of Aurora kinase inhibitors in the spindle assembly checkpoint' Frontiers in Bioscience, vol 15, no. 1, pp. 249-258., 10.2741/3619

Alzahrani, EO, Davidson, FA & Dodds, N 2010, 'Travelling waves in near-degenerate bistable competition models' Mathematical Modelling of Natural Phenomena, vol 5, no. 5, pp. 13-35., 10.1051/mmnp/20105502

1.6. 2009

Rosling, A, Roose, T, Herrmann, AM, Davidson, FA, Finlay, RD & Gadd, GM 2009, 'Approaches to modelling mineral weathering by fungi' Fungal Biology Reviews, vol 23, no. 4, pp. 138-144., 10.1016/j.fbr.2009.09.003

1.7. 2008

Mistry, HB, MacCallum, DE, Jackson, RC, Chaplain, MAJ & Davidson, FA 2008, 'Modeling the temporal evolution of the spindle assembly checkpoint and role of Aurora B kinase' Proceedings of the National Academy of Sciences USA, vol 105, no. 51, pp. 20215-20220., 10.1073/pnas.0810706106

Davidson, FA 2008, 'Theoretical and mathematical ecology' Fungal Ecology, vol 1, pp. 107-107., 10.1016/j.funeco.2009.01.001

Smith, MJ, Kobine, JJ & Davidson, FA 2008, 'Free and forced motion in an asymmetric liquid-column oscillator' Proceedings of the Royal Society of London A : Mathematical, Physical and Engineering Sciences, vol 464, no. 2092, pp. 905-922., 10.1098/rspa.2007.0375

Mistry, H, Davidson, F, Chaplain, M & Jackson, R 2008, 'A pharmacodynamic model of the spindle assembly checkpoint and the action of the aurora kinase inhibitors' 99th AACR Annual Meeting, San Diego, CA, United States, 12/04/08 - 16/04/08, pp. 1642.

Davidson, FA 2008, 'Theoretical and mathematical ecology (Editorial)' Fungal Ecology, vol 1, no. 4, pp. 107., doi:10.1016/j.funeco.2009.01.001

1.8. 2007

Davidson, FA 2007, 'Berkeley Award Lecture: mathematical modelling of the form and function of fungal mycelia'. in G Gadd, SC Watkinson & PS Dyer (eds), Fungi in the environment. British Mycological Society Symposia, no. 25, Cambridge University Press, pp. 58-74., 10.2277/0521850290

Boswell, GP & Davidson, FA 2007, 'Diffusion fronts in enzyme-catalysed reactions' Journal of Engineering Mathematics, vol 59, no. 2, pp. 157-169., 10.1007/s10665-007-9142-x

Bowen, AD, Davidson, FA, Keatch, R & Gadd, GM 2007, 'Effect of nutrient availability on hyphal maturation and topographical sensing in Aspergillus niger' Mycoscience, vol 48, no. 3, pp. 145-151., 10.1007/s10267-007-0352-x

Davidson, FA & Rynne, BP 2007, 'Eigenfunction expansions in L2 spaces for boundary value problems on time-scales' Journal of Mathematical Analysis and Applications, vol 335, no. 2, pp. 1038-1051., 10.1016/j.jmaa.2007.01.100

Davidson, FA & Dodds, N 2007, 'Existence of positive solutions due to non-local interactions in a class of nonlinear boundary value problems' Methods and Applications of Analysis, vol 14, no. 1, pp. 15-28.

Bowen, AD, Davidson, FA, Keatch, R & Gadd, GM 2007, 'Induction of contour sensing in Aspergillus niger by stress and its relevance to fungal growth mechanics and hyphal tip structure' Fungal Genetics and Biology, vol 44, no. 6, pp. 484-491., 10.1016/j.fgb.2006.11.012

Davidson, FA 2007, 'Mathematical modelling of mycelia: a question of scale' Fungal Biology Reviews, vol 21, no. 1, pp. 30-41., 10.1016/j.fbr.2007.02.005

Davidson, FA & Dodds, N 2007, 'Properties of eigenfunctions of non-local operators'. in Proceedings of minisymposia and contributed talks of EQUADIFF-11: International conference on differential equations Czecho-Slovak series. Comenius University Press, pp. 57-66, International Conference on Differential Equations: Czecho-Slovak series, Bratislava, Slovakia, 25-29 July.

Davidson, FA & Rynne, BP 2007, 'Self-adjoint boundary-value problems on time-scales' Electronic Journal of Differential Equations, vol 2007, no. 175, pp. 1-10.

Boswell, GP, Jacobs, H, Ritz, K, Gadd, GM & Davidson, FA 2007, 'The development of fungal networks in complex environments' Bulletin of Mathematical Biology, vol 69, no. 2, pp. 605-634., 10.1007/s11538-005-9056-6

1.9. 2006

Xu, R, Chaplain, MAJ & Davidson, FA 2006, 'Travelling wave and convergence in stage-structured reaction-diffusion competitive models with nonlocal delays' Chaos, Solitons & Fractals, vol 30, no. 4, pp. 974-992., 10.1016/j.chaos.2005.09.022

Davidson, FA & Dodds, N 2006, 'Spectral properties of non-local uniformly-elliptic operators' Electronic Journal of Differential Equations, vol 2006, no. 126, pp. 1-15.

Xu, R, Chaplain, MAJ & Davidson, FA 2006, 'A Lotka-Volterra type food chain model with stage structure and time delays' Journal of Mathematical Analysis and Applications, vol 315, no. 1, pp. 90-105., 10.1016/j.jmaa.2005.09.090

Xu, R, Chaplain, MAJ & Davidson, FA 2006, 'Global convergence of a reaction-diffusion predator-prey model with stage structure for the predator' Applied Mathematics and Computation, vol 176, no. 1, pp. 388-401., 10.1016/j.amc.2005.09.028

Xu, R, Chaplain, MAJ & Davidson, FA 2006, 'Periodic solutions of a Lotka-Volterra type multi-species population model with time delays' Mathematische Nachrichten, vol 279, no. 8, pp. 911-927., 10.1002/mana.200310402

Davidson, FA & Dodds, N 2006, 'Spectral properties of non-local differential operators' Applicable Analysis, vol 85, no. 6-7, pp. 717-734., 10.1080/00036810600555171

1.10. 2005

Smith, MJ, Kobine, JJ & Davidson, FA 2005, 'Controlling beat phenomena in coupled systems using asymmetric tuned liquid column dampers'. in SK Chakrabarti, S Hernandez & CA Brebbia (eds), Fluid structure interaction and moving boundary problems. vol. 84, WIT TRANSACTIONS ON THE BUILT ENVIRONMENT, vol. 84, WIT Press, SOUTHAMPTON, pp. 457-464, 3rd International Conference on Fluid Structure Interaction/8th International Conference on Computational Modelling and Experimental Measurements of Free and Moving Boundary Problems, Coruna, Spain, 19-21 September.

Xu, R, Chaplain, MAJ & Davidson, FA 2005, 'Global stability of a stage-structured predator-prey model with prey dispersal' Applied Mathematics and Computation, vol 171, no. 1, pp. 293-314., 10.1016/j.amc.2005.01.055

Xu, R, Chaplain, MAJ & Davidson, FA 2005, 'Modelling and analysis of a competitive model with stage structure' Mathematical and Computer Modelling, vol 41, no. 2-3, pp. 159-175., 10.1016/j.mcm.2004.08.003

Xu, R, Chaplain, MAJ & Davidson, FA 2005, 'Periodic solutions for a predator-prey model with Holling-type functional response and time delays' Applied Mathematics and Computation, vol 161, no. 2, pp. 637-654., 10.1016/j.amc.2003.12.054

Xu, R, Chaplain, MAJ & Davidson, FA 2005, 'Permanence and periodicity of a delayed ratio-dependent predator-prey model with stage structure' Journal of Mathematical Analysis and Applications, vol 303, no. 2, pp. 602-621., 10.1016/j.jmaa.2004.08.062

1.11. 2004

Xu, R, Chaplain, MAJ & Davidson, FA 2004, 'Persistence and global stability of a ratio-dependent predator-prey model with stage structure' Applied Mathematics and Computation, vol 158, no. 3, pp. 729-744., 10.1016/j.amc.2003.10.012

Jacobs, H, Boswell, GP, Scrimgeour, CM, Davidson, FA, Gadd, GM & Ritz, K 2004, 'Translocation of carbon by Rhizoctonia solani in nutritionally-heterogeneous microcosms' Mycological Research, vol 108, no. 4, pp. 453-462., 10.1017/S0953756204009840

Xu, R, Chaplain, MAJ & Davidson, FA 2004, 'Persistence and stability of a stage-structured predator-prey model with time delays' Applied Mathematics and Computation, vol 150, no. 1, pp. 259-277., 10.1016/S0096-3003(03)00226-1

Xu, R, Chaplain, MAJ & Davidson, FA 2004, 'Global asymptotic stability of periodic solution for a cooperative system with time delays' Indian Journal of Pure and Applied Mathematics, vol 35, no. 7, pp. 915-936.

Xu, R, Chaplain, MAJ & Davidson, FA 2004, 'Global stability of a Lotka-Volterra type predator-prey model with stage structure and time delay' Applied Mathematics and Computation, vol 159, no. 3, pp. 863-880., 10.1016/j.amc.2003.11.008

Xu, R, Chaplain, MAJ & Davidson, FA 2004, 'Periodic solution for a three-species Lotka-Volterra food-chain model with time delays' Mathematical and Computer Modelling, vol 40, no. 7-8, pp. 823-837., 10.1016/j.mcm.2004.10.011

Xu, R, Chaplain, MAJ & Davidson, FA 2004, 'Periodic solution of a Lotka-Volterra predator-prey model with dispersion and time delays' Applied Mathematics and Computation, vol 148, no. 2, pp. 537-560., 10.1016/S0096-3003(02)00918-9

Xu, R, Chaplain, MAJ & Davidson, FA 2004, 'Periodic solutions for a delayed predator-prey model of prey dispersal in two-patch environments' Nonlinear Analysis: Real World Applications, vol 5, no. 1, pp. 183-206., 10.1016/S1468-1218(03)00032-4

Xu, R, Chaplain, MAJ & Davidson, FA 2004, 'Periodic solutions of a discrete nonautonomous Lotka-Volterra predator-prey model with time delays' Discrete and Continuous Dynamical Systems: Series B, vol 4, no. 3, pp. 823-831., 10.3934/dcdsb.2004.4.823

Xu, R, Davidson, F & Chaplain, MAJ 2004, 'Periodic solutions of a discrete time three-species Lotka-Volterra food-chain system' Nonlinear Functional Analysis and Applications, vol 9, no. 3, pp. 429-440.

Xu, R, Chaplain, MAJ & Davidson, FA 2004, 'Periodic solutions of a predator-prey model with stage structure for predator' Applied Mathematics and Computation, vol 154, no. 3, pp. 847-870., 10.1016/S0096-3003(03)00753-7

Chaplain, MAJ, Xu, R & Davidson, FA 2004, 'Persistence and periodicity of a delayed ratio-dependent predator-prey model with stage structure and prey dispersal' Applied Mathematics and Computation, vol 159, no. 3, pp. 823-846., 10.1016/j.amc.2003.11.006

Stoleriu, I, Davidson, FA & Liu, JL 2004, 'Quasi-steady state assumptions for non-isolated enzyme-catalyzed reactions' Journal of Mathematical Biology, vol 48, no. 1, pp. 82-104., 10.1007/s00285-003-0225-7

1.12. 2003

Boswell, GP, Jacobs, H, Davidson, FA, Gadd, GM & Ritz, K 2003, 'A positive numerical scheme for a mixed-type partial differential equation model for fungal growth' Applied Mathematics and Computation, vol 138, no. 2-3, pp. 321-340., 10.1016/S0096-3003(02)00121-2

Boswell, GP, Jacobs, H, Davidson, FA, Gadd, GM & Ritz, K 2003, 'Growth and function of fungal mycelia in heterogeneous environments' Bulletin of Mathematical Biology, vol 65, no. 3, pp. 447-477., 10.1016/S0092-8240(03)00003-X

1.13. 2002

Jacobs, H, Boswell, GP, Harper, FA, Ritz, K, Davidson, FA & Gadd, GM 2002, 'Solubilization of metal phosphates by Rhizoctonia solani' Mycological Research, vol 106, no. 12, pp. 1468-1479., 10.1017/S0953756202006901

Boswell, GP, Jacobs, H, Davidson, FA, Gadd, GM & Ritz, K 2002, 'Functional consequences of nutrient translocation in mycelial fungi' Journal of Theoretical Biology, vol 217, no. 4, pp. 459-477., 10.1006/jtbi.2002.3048

Davidson, FA & Liu, J 2002, 'Global stability of the attracting set of an enzyme-catalysed reaction system' Mathematical and Computer Modelling, vol 35, no. 13, pp. 1467-1481., 10.1016/S0895-7177(02)00098-5

Davidson, FA, Xu, R & Liu, J 2002, 'Existence and uniqueness of limit cycles in an enzyme-catalysed reaction system' Applied Mathematics and Computation, vol 127, no. 2-3, pp. 165-179., 10.1016/S0096-3003(01)00065-0

Jacobs, H, Boswell, GP, Ritz, K, Davidson, FA & Gadd, GM 2002, 'Solubilization of calcium phosphate as a consequence of carbon translocation by Rhizoctonia solani' FEMS Microbiology Ecology, vol 40, no. 1, pp. 65-71., 10.1111/j.1574-6941.2002.tb00937.x

Davidson, FA & Rynne, BP 2002, 'Global bifurcation on time scales' Journal of Mathematical Analysis and Applications, vol 267, no. 1, pp. 345-360., 10.1006/jmaa.2001.7780

Xu, R, Davidson, FA & Chaplain, MAJ 2002, 'Persistence and stability for a two species ratio-dependent predator-prey system with distributed time delay' Journal of Mathematical Analysis and Applications, vol 269, no. 1, pp. 256-277., 10.1016/S0022-247X(02)00020-3

1.14. 2001

Rui, X, Chaplain, MAJ & Davidson, FA 2001, 'Global asymptotic stability in a nonautonomous n-species Lotka-Volterra predator-prey system with infinite delays' Applicable Analysis, vol 80, no. 1-2, pp. 107-126., 10.1080/00036810108840983

Gourley, SA, Chaplain, MAJ & Davidson, FA 2001, 'Spatio-temporal pattern formation in a nonlocal reaction-diffusion equation' Dynamical Systems, vol 16, no. 2, pp. 173-192., 10.1080/14689360116914

Davidson, FA & Gourley, SA 2001, 'The effects of temporal delays in a model for a food-limited diffusing population' Journal of Mathematical Analysis and Applications, vol 261, no. 2, pp. 633-648., 10.1006/jmaa.2001.7563

1.15. 2000

Davidson, FA & Rynne, BP 2000, 'Asymptotic Oscillations of Continua of Positive Solutions of a Semilinear Sturm–Liouville Problem' Journal of Mathematical Analysis and Applications, vol 252, no. 2, pp. 617-630., 10.1006/jmaa.2000.7009

Davidson, FA & Olsson, S 2000, 'Translocation Induced Outgrowth of Fungi in Nutrient-free Environments' Journal of Theoretical Biology, vol 205, no. 1, pp. 73-84., 10.1006/jtbi.2000.2045

Davidson, FA & Rynne, BP 2000, 'A priori bounds and global existence of solutions of the steady-state Sel'kov model' Proceedings of the Royal Society of Edinburgh, Section A : Mathematics, vol 130, no. 3, pp. 507-516., 10.1017/S0308210500000275

Davidson, FA, Anderson, ARA & Chaplain, MAJ 2000, 'Steady state solutions of a generic model for the formation of capillary networks' Applied Mathematics Letters, vol 13, no. 5, pp. 127-132., 10.1016/S0893-9659(00)00044-6

1.16. 1999

Davidson, FA 1999, 'Global Secondary Bifurcation in a Non-linear Boundary Value Problem' Journal of Mathematical Analysis and Applications, vol 240, no. 1, pp. 80-91., 10.1006/jmaa.1999.6591

1.17. 1998

Davidson, FA 1998, 'Modelling the Qualitative Response of Fungal Mycelia to Heterogeneous Environments' Journal of Theoretical Biology, vol 195, no. 3, 12, pp. 281., 10.1006/jtbi.1998.0739

Davidson, FA & Park, AW 1998, 'A mathematical model for fungal development in heterogeneous environments' Applied Mathematics Letters, vol 11, no. 6, pp. 51-56., 10.1016/S0893-9659(98)00102-5

Davidson, FA 1998, 'Chaotic Wakes and Other Wave-Induced Behavior in a System of Reaction–Diffusion Equations' International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol 8, no. 6, pp. 1303-1313., 10.1142/S0218127498001005

Chaplain, M, Kuznetsov, VA, James, ZH, Davidson, F & Stepanova, LA 1998, 'Spatio-temporal dynamics of the immune system response to cancer'. in H Mary Ann, S Gieri & W Glenn F. (eds), Mathematical models in medical and health science. Vanderbilt University Press, International Conference on Mathematical Models in Medical and Health Sciences, Nashville, United States, 28-31 May.

1.18. 1997

Davidson, FA, Sleeman, BD & Crawford, JW 1997, 'Travelling waves in a reaction-diffusion system modelling fungal mycelia' IMA Journal of Applied Mathematics, vol 58, no. 3, pp. 237-257., 10.1093/imamat/58.3.237

Davidson, FA, Sleeman, BD, Rayner, ADM, Crawford, JW & Ritz, K 1997, 'Travelling waves and pattern formation in a model for fungal development' Journal of Mathematical Biology, vol 35, no. 5, pp. 589-608., 10.1007/s002850050067

1.19. 1996

Davidson, FA, Sleeman, BD, Rayner, ADM, Crawford, JW & Ritz, K 1996, 'Large-scale behavior of fungal mycelia' Mathematical and Computer Modelling, vol 24, no. 10, pp. 81-87., 10.1016/S0895-7177(96)00166-5

Davidson, FA, Sleeman, BD, Rayner, ADM, Crawford, JW & Ritz, K 1996, 'Context-dependent macroscopic patterns in growing and interacting mycelial networks' Proceedings of the Royal Society B, vol 263, no. 1372, pp. 873-880., 10.1098/rspb.1996.0129

Davidson, FA & Rynne, BP 1996, 'Local and global behaviour of steady-state solutions of the Sel'kov model' IMA Journal of Applied Mathematics, vol 56, no. 2, pp. 145-155., 10.1093/imamat/56.2.145

1.20. 1995

Brown, KJ & Davidson, FA 1995, 'Global bifurcation in the Brusselator system' Nonlinear Analysis, vol 24, no. 12, pp. 1713-1725., 10.1016/0362-546X(94)00218-7