Dr Fordyce Davidson

Publications

2012

Boswell G.P. and Davidson F.A., Modelling hyphal networks, Fungal Biology Reviews 26, 30-38 (2012) pdf

Alzahrani, E.O., Davidson F.A. and Dodds, N., A 3-species competition model for biocontrol, Applied Math. Comput. 218, 9690-9698 (2012) pdf

Davidson F.A., Is cell fusion driven by excitation?, Bioessays, 34, 258 (2012)

2011

Alzahrani, E.O., Davidson F.A. and Dodds, N., Reversing invasion in bistable systems, Journal of Mathematical Biology, Online

Davidson F.A., Boswell, G.P., Fischer M.W., Heaton, L. Hofstadler D. and Roper M., Mathematical modelling of fungal growth and function, IMA Fungus,  2 33-37 (2011) pdf.

2010

Kamei, H., Jackson, R.C., Zheleva, D. and Davidson, F.A., An integrated pharmacokinetic-pharmacodynamic model for an Aurora kinase inhibitor, J. Pharmacokinetics and Pharmacodynamics, 37 404-434, (2010) pdf.

Alzahrani, E.O., Davidson F.A. and Dodds, N., Travelling waves in near-degenerate bistable competition models, Mathematical Modelling of Natural Phenomena, 5 (5) 13-35, (2010) pdf.

Davidson, F.A., A Blueprint for polarised growth, Microbiology Today February, 34-37, (2010) pdf

Mistry, H., MacCallum, D.E., Jackson, R.C., Chaplain, M.A.J., Davidson, F.A., A Pharmacodynamic model of Aurora kinase inhibitors in the spindle assembly checkpoint, Frontiers in Bioscience, 15 249-258 (2010).pdf

2009

Rosling, A., Roose, T., Herrmann, A.M., Davidson, F.A., Finlay, R.D. and Gadd, G.M., Approaches to modelling mineral weathering by fungi, Fungal Biology Reviews, 23 (4) 138-144 (2009)pdf

2008

Davidson, F.A., Theoretical and mathematical ecology, Fungal Ecology, 1, 107 (editorial for special edition) (2008)pdf

Mistry, H.B., MacCallum, D.E., Jackson, R.C., Chaplain, M.A.J. and Davidson, F.A. Modelling the Role of Aurora Kinases in Centrosome Separation and the Spindle Assembly Checkpoint, PNAS 105 (51), 20215-20220 (2008) pdf

Smith M., Kobine J.J., & Davidson F.A., Free and forced motion in an asymmetric liquid-column oscillator, Proc. R. Soc. A. 464:905-922 (2008).pdf

Mistry, H.B., Davidson, F.A., Chaplain, M.A.J. and Jackson, R.C., A pharmacodynamic model of the spindle assembly checkpoint and the action of the aurora kinase inhibitors, AARC Meeting Abstracts April 2008, 1642 (2008) Link

2007

Davidson F.A. and Dodds, N., Existence of positive solutions due to nonlocal interactions in a class of nonlinear boundary value problems, Meth. Appl. Anal. , 14, 15-28, (2007).pdf

Davidson F.A. & Rynne, B.P., Self-adjoint boundary value problems on time-scales, Elect. J. Diff. Eqns. Vol. 2007(2007), No. 175, pp. 1-10. pdf

Boswell, G.P. and Davidson, F.A., Diffusion fronts in enzyme-catalysed reactions J. Eng. Math.59: 157-169 (2007) (Invited submission) pdf

Boswell G.P., Jacobs H., Ritz K., Gadd G.M. & Davidson F.A., The development of fungal networks in complex environments, Bull. Math. Biol., 69, 605-634 (2007) pdf

Davidson F.A. and Rynne, B.P., Eigenfunction expansions in L^2 spaces for boundary value problems on time-scales, J. Math. Anal. App. 335, 1038-1051 (2007) pdf

Bowen, A. D., Davidson, F. A., Keatch, R., Gadd, G. M., Induction of contour sensing in Aspergillus niger by stress and its relevance to fungal growth mechanics and hyphal tip structure. Fungal Genetics and Biology 44: 484-491 (2007). pdf

Bowen, A. D., Davidson, F. A., Keatch, R., Gadd, G. M., Effect of nutrient availability on hyphal maturation and topographical sensing in Aspergillus niger, Mycoscience 48: 145-151 (2007) pdf.

Davidson, F.A. Mathematical modelling of the form and function of fungal mycelia, Fungi in the Environment , Gadd, Watkins and Dyer (eds.) Cambridge University Press, Cambridge (2007).

Davidson, F.A. Mathematical modelling of mycelia: a question of scale, Fungal Biology Reviews 21: 30-41, (2007) pdf.

2006

Xu R, Chaplain MAJ, Davidson FA A Lotka-Volterra type food chain model with stage structure and time delays JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 315 (1): 90-105 (2006).pdf

Davidson F.A. and Dodds, N., Spectral properties of non-local differential operators, Applicable Analysis 85, Number 6-7, 717 - 734 (2006) pdf.

Xu R, Chaplain MAJ, Davidson FA Global convergence of a reaction-diffusion predator-prey model with stage structure for the predator APPLIED MATHEMATICS AND COMPUTATION 176 (1): 388-401 (2006).

Xu R, Chaplain MAJ, Davidson FA Periodic solutions of a Lotka-Volterra type multi-species population model with time delays MATHEMATISCHE NACHRICHTEN 279 (8): 911-927 (2006).

Xu R, Chaplain MAJ, Davidson FA Travelling wave and convergence in stage-structured reaction-diffusion competitive models with nonlocal delays CHAOS SOLITONS & FRACTALS 30 (4): 974-992 (2006).

Davidson, F.A. and Rynne, B.P., The formulation of second-order boundary value problems on time-scales Advances in Difference Equations (Invited submission) vol 2006, Article ID 31430: (2006) 10 pages pdf.

Davidson F.A. and Dodds, N., Spectral properties of non-local uniformly elliptic operators, Elect. J. Diff. Equ. Vol. 2006 (126): 1-15 (2006) pdf.

2005

Rui X, Chaplain MAJ, Davidson FA Periodic solutions for a predator-prey model with Holling-type functional response and time delays APPLIED MATHEMATICS AND COMPUTATION 161 (2): 637-654 (2005).

Xu R, Chaplain MAJ, Davidson FA Permanence and periodicity of a delayed ratio-deplendent predator-prey model with stage structure JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 303 (2): 602-621 (2005).

Xu R, Chaplain MAJ, Davidson FA Modelling and analysis of a competitive model with stage structure MATHEMATICAL AND COMPUTER MODELLING 41 (2-3): 159-175 (2005).

Xu R, Chaplain MAJ, Davidson FA Global stability of a stage-structured predator-prey model with prey dispersal APPLIED MATHEMATICS AND COMPUTATION 171 (1): 293-314 (2005).

Xu R, Chaplain MAJ, Davidson FA, APPLIED MATHEMATICS AND COMPUTATION 161 (2): 637-654 (2005).

Stoleriu J., Davidson F.A. and Liu J., Effects of periodic input on the quasi-steady state assumptions for enzyme-catalysed reactions J. Math. Biol., 50, 115-132 (2005) pdf.

2004

Xu R, Chaplain MAJ, Davidson FA Periodic solution of a Lotka-Volterra predator-prey model with dispersion and time delays APPLIED MATHEMATICS AND COMPUTATION 148 (2): 537-560 (2004).

Xu R, Chaplain MAJ, Davidson FA Periodic solutions for a delayed predator-prey model of prey dispersal in two-patch environments NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS 5 (1): 183-206 (2004).

Xu R, Chaplain MAJ, Davidson FA Periodic solutions of a predator-prey model with stage structure for predator APPLIED MATHEMATICS AND COMPUTATION 154 (3): 847-870 (2004).

Xu R, Chaplain MAJ, Davidson FA Persistence and global stability of a ratio-dependent predator-prey model with stage structure APPLIED MATHEMATICS AND COMPUTATION 158 (3): 729-744 (2004).

Xu R, Chaplain MAJ, Davidson FA Persistence and periodicity of a delayed ratio-dependent predator-prey model with stage structure and prey dispersal APPLIED MATHEMATICS AND COMPUTATION 159 (3): 823-846 (2004).

Rui X, Chaplain MAJ, Davidson FA Periodic solution for a three-species Lotka-Volterra food-chain model with time delays MATHEMATICAL AND COMPUTER MODELLING 40 (7-8): 823-837 (2004).

Xu R, Chaplain MAJ, Davidson FA Periodic solutions of a discrete nonautonomous Lotka-Volterra predator-prey model with time delays DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B 4 (3): 823-831 (2004).

Xu R, Chaplain MAJ, Davidson FA Persistence and stability of a stage-structured predator-prey model with time delays APPLIED MATHEMATICS AND COMPUTATION 150 (1): 259-277 (2004).

Xu R., Chaplain, M.A.J. and Davidson F.A., Periodic solutions of a Lotka-Volterra predator-prey model with dispersion and time delays, Appl. Math. Compt. , 148: 537-560 (2004).

Xu R., Chaplain, M.A.J. and Davidson F.A., Persistance and stability of a stage-structured predator-prey model with time delays, Appl. Math. Compt. , 150: 259-277 (2004).

Stoleriu J., Davidson F.A. and Liu J., Quasi-steady state assumptions for non-isolated enzyme-catalyzed reactions, J. Math. Biol. 48: 82-104 (2004) pdf.

Jacobs H, Boswell GP, Scrimgeour CM, Davidson FA, Gadd GM, Ritz K, Translocation of carbon by Rhizoctonia solani in nutritionally-heterogeneous microcosms, Mycological Research 108: 453-462 (2004).

Davidson F.A. and Rynne, B.P., Curves of positive solutions of boundary value problems on time-scales J. Math. Anal. Appl. 300: 491-504 (2004) pdf.

Rui X, Chaplain MAJ, Davidson FA Global asymptotic stability of periodic solution for a cooperative system with time delays INDIAN J PURE AP MAT 35: 915-936 (2004).

Xu R., Chaplain, M.A.J. and Davidson F.A., Periodic solutions of a predator-prey model with stage-structure for predator, Appl. Math. Compt. 154: 847-870 (2004).

Xu R., Chaplain, M.A.J. and Davidson F.A., Persistance and global stability of a ratio-depedent predator-prey model with stage-structure, Appl. Math. Compt. 158: 729-744 (2004).

Xu R., Chaplain, M.A.J. and Davidson F.A., Periodic solutions of a discrete time three-species lotka-Volterra food-chain system, Nonlinear Funct. Anal. & Appl. 9: 429-440 (2004).

Xu R., Chaplain, M.A.J. and Davidson F.A., Global stability of a Lotka-Volterra type predator-prey model with stage structure and time delay, Appl. Math. Compt. 159: 863-880 (2004).

2003

Boswell G.P., Jacobs H., Davidson F.A., Gadd G.M. and Ritz K., A positive numerical scheme for a mixed-type partial differential equation model for fungal growth, Appl. Math. Comp. 138: 321-340 (2003). pdf

Boswell G.P., Jacobs H., Davidson F.A., Gadd G.M. and Ritz K., Growth and function of fungal mycelia in heterogeneous environments, Bull. Math. Biol. 65: 447-477 (2003)pdf.

Boswell G.P., Jacobs H., Gadd G.M., Ritz K. and Davidson F.A., A mathematical approach to studying fungal mycelia, Mycologist 17: 165-171 (2003).

2002

Davidson F.A., Xu R. & Liu J.Existence and Uniqueness of limit cycles in an enzyme-catalysed reaction system Appl. Math. Comp. 127: 165-179 (2002).

Davidson F.A. and Rynne, B.P., Global bifurcation on time scales J. Math. Anal. Appl. 267: 345-360 (2002).

Jacobs H., Boswell G.P.,Ritz K., Davidson F.A. and Gadd G.M., Solubilization of calcium phosphate as a consequence of carbon translocation by Rhizoctonia solani, FEMS Microbiology Ecology 40(1):65-71 (2002)pdf.

Xu R., Davidson F.A. and Chaplain, M.A.J., Persistence and stability for a two-species ratio-dependent predator-prey system with distributed time-delay, J. Math. Anal. Appl. 269 (1): 256-277 (2002).

Davidson F.A., A remark on the global structure of the solution set for a generic class of non-linear eigenvalue problems, Comm. Appl. Anal. 6 (4):449 (2002).

Boswell G.P., Jacobs H., Davidson F.A., Gadd G.M. and Ritz K., Functional consequences of translocation in mycelial fungi, J. theor. Biol. 217 (4): 459-477 (2002)pdf.

Davidson F.A. & Liu J., Global stability of the attracting set of an enzyme-catalysed reaction system Mathl. Compt. Modelling, 35 (13): 1467-1481 (2002).

Xu R., Chaplain, M.A.J. and Davidson F.A., Global asymptotic stability in a non-autonomous n-species Lotka-Volterra perdator-prey system with infinite delays, Applicable Analysis 80: 107-126 (2002).

Jacobs H., Boswell G.P., Harper, F.A., Ritz K., Davidson F.A. and Gadd G.M., Solubilization of metal phosphates by Rhizoctonia solani, Mycological Research 106 (12) : 1468-1479 (2002). pdf

2001

Gourley S.A., Chaplain M.A.J. & Davidson F.A., Spatio-temporal Pattern Formation in a Nonlocal Reaction-diffusion Equation, Dynamical Systems and Applications 16: 173-192 (2001).

Davidson F.A. & Gourley S.A., The effects of temporal delays in a model for a food-limited diffusing population, J. Math. Anal. Appl. 261: 633-648 (2001).

2000

Davidson F.A., Anderson, A.R.A. and Chaplain, M.A.J., Steady State Solutions of a Generic Model for the Formation of Capillary Networks, Appl. Math. Lett. 13 (5): 127-132 (2000).

Davidson F.A. & Olsson S., Translocation induced outgrowth of fungi in nutrient free environments, J. Theor. Biol. 205 (1): 73-84 (2000). pdf

Davidson F.A. & Rynne B.P., A-priori bounds and global existence of solutions of the steady state Sel'kov Model, Proc. Roy. Soc. Ed. A 130A: 507-516 (2000).

Davidson F.A. & Rynne B.P., Asymptotic oscillations of continua of positive solutions of a semilinear Sturm-Liouville problem, J. Math. Anal. Appl. 252: 617-630 (2000). pdf

Pre-2000

Brown K.J. & Davidson F.A., Global bifurcation in the Brusselator System, Nonlinear Analysis, Theory, Methods & Applications 24 (12): 1713-1725 (1995).

Davidson F.A. & Rynne B.P., Local and global behaviour of steady state solutions of the Sel'kov model, IMA J. of Appl. Math. 56: 145-155 (1996).

Davidson F.A., Sleeman B.D., Rayner A.D.M., Crawford J.W. & Ritz K., Context-dependent macroscopic patterns in growing and interacting mycelial networks, Proc. R. Soc. Lond. B 263: 873-880 (1996).

Davidson F.A., Sleeman B.D., Rayner A.D.M., Crawford J.W. & Ritz K., Large-scale behaviour of fungal mycelia, Mathl. Compt. Modelling 24 (10): 81-87 (1996).

Davidson F.A., Sleeman B.D., Rayner A.D.M., Crawford J.W. & Ritz K., Travelling waves and pattern formation in a model for fungal development, J. of Math. Biol. 35: 589-608 (1997).

Davidson F.A., Sleeman B.D. & Crawford J.W., Travelling waves in a reaction-diffusion system modelling fungal mycelia, IMA J. of Appl. Math. 58: 237-257 (1997).

Davidson F.A. & Park A.W., A Mathematical Model for Fungal Development in Heterogeneous Environments, Appl. Maths. Lett. 11: 51-56 (1998).

Davidson F.A., Chaotic wakes and other wave-induced behaviour in a system of reaction-diffusion equations, Int. J. Bifurcation and Chaos 8: 1303-1313 (1998).

Davidson F.A., Modelling the qualitative response of fungal mycelial to heterogeneous environments, J. theor. Biology 195: 281-292 (1998).

Davidson F.A., Global secondary bifurcation in a non-linear boundary value problem, J. Math. Anal. Appl. 204: 80-91 (1999).