464:905-922 (2008).pdf
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)
Davidson F.A. and Dodds, N., Spectral properties of non-local
differential operators, Applicable Analysis 85, Number 6-7, 717 - 734 (2006).
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: 10 pages (2006).
Davidson F.A. and Dodds, N., Spectral properties of non-local uniformly elliptic operators, Elect. J. Diff. Equ. Vol. 2006 (126): 1-15 (2006).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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