Dr Isaac Towers

Undergraduate Coordinator
02 6268 8217
02 6268 8786


Room 132a PEMS South (Bldg 26) School of Science, UNSW Canberra, Australian Defence Force Academy, PO Box 7916, Canberra BC ACT 2610, AUSTRALIA


Dr Isaac Towers is a Senior Lecturer in the School of Physical, Environmental and Mathematical Sciences at UNSW Canberra.

Current Research

  • Stochastic differential equations
  • Ecological modelling
  • Nonlinear dynamics
  • Combustion waves

PhD Opportunities and Scholarships

If you are interested in PhD research in Applied Mathematics contact: Dr Isaac Towers, i.towers@adfa.edu.au

Current Postgraduate Students

  • Chad Anderson (PhD) - Analysis of Population Dynamics subject to Environmental Changes
  • Paul Hartlipp (MPhil) - An investigation of coastal sea surface measurements for the Maritime Continent using SARAL/Altika Satellite measurements
  • Luis Mijangos Aruajo (PhD) - Genetics for Forecasting and Managing Biodiversity
  • Rashed Saifuddin (PhD) - Developing realistic models for stressed ecosystems
  • Chris Thomas (PhD) - Incorporation of spotting and intrinsic fire dynamics in a coupled atmosphere-fire modelling framework
  • Hilyati Zazali (PhD) - Stochastic bushfire spread modelling

Past Postgraduate Students

  1. Andrew Robards (MPhil) - The cost efficiency of different freight modes
  2. Dr. Zhejun Huang  (PhD) - Combustion waves in a two-stage sequential exothermic-endothermic reaction scheme
  3. Chad Anderson (MPhil) - Population Dynamics in a Stochastic Environment
  4. Tom Dose (Honours) - Discrete population dynamics with varying carrying capacity
  5. Dr. Hamizah Safuan - Mathematical Analysis of Population Growth Subject to Environmental Change (2014 Ria de Groot Prize Winner)
  6. Yang Sun (MPhil) -  Soliton Dynamics in Frequency-Modulated Lattices



Journal articles

Amirian MM; Towers IN; Jovanoski Z; Irwin AJ, 2020, 'Memory and mutualism in species sustainability: A time-fractional Lotka-Volterra model with harvesting', Heliyon, vol. 6, pp. e04816 - e04816, http://dx.doi.org/10.1016/j.heliyon.2020.e04816

Huang Z; Sidhu HS; Towers IN; Jovanoski Z; Watt S; Gubernov VV, 2020, 'Properties of nonadiabatic combustion waves in competitive exothermic reactions', Applied Mathematical Modelling, vol. 77, pp. 1216 - 1228, http://dx.doi.org/10.1016/j.apm.2019.09.010

Ang TK; Safuan HM; Sidhu HS; Jovanoski Z; Towers IN, 2019, 'Impact of Harvesting on a Bioeconomic Predator–Prey Fishery Model Subject to Environmental Toxicant', Bulletin of Mathematical Biology, vol. 81, pp. 2748 - 2767, http://dx.doi.org/10.1007/s11538-019-00627-8

Watt SD; Sidhu HS; Jovanoski Z; Towers IN; Huang Z, 2019, 'Watershed initial conditions for propagating waves in a system with bistability: A weight-function approach', Applied Mathematics Letters, vol. 91, pp. 106 - 112, http://dx.doi.org/10.1016/j.aml.2018.11.018

Huang Z; Sidhu H; Towers I; Jovanoski Z; Watt S, 2018, 'On the route to extinction in non-adiabatic flames from competitive exothermic reactions', Mathematical Modelling of Natural Phenomena, vol. 13, http://dx.doi.org/10.1051/mmnp/2018047

Huang Z; Sidhu H; Towers I; Jovanoski Z; Gubernov V, 2017, 'Stability analysis of combustion waves for competitive exothermic reactions using Evans function', Applied Mathematical Modelling, vol. 54, pp. 347 - 360, http://dx.doi.org/10.1016/j.apm.2017.09.055

Dose T; Jovanoski Z; Safuan HM; Sidhu H; Towers I, 2017, 'Dynamics of a Discrete Non-Autonomous Ricker Model', Journal of Engineering and Applied Science, vol. 12, pp. 2304 - 2309, http://dx.doi.org/10.3923/jeasci.2017.2304.2309

Saifuddin R; Jovanoski Z; Safuan HM; Towers I; Sidhu H, 2017, 'Stability of a Population in a Model with Delayed Environmental Response', Journal of Engineering and Applied Sciences, vol. 12, pp. 2299 - 2303, http://dx.doi.org/10.3923/jeasci.2017.2299.2303

Huang Z; Sidhu HS; Towers IN; Jovanoski Z; Gubernov VV, 2017, 'Properties of combustion waves in a model with competitive exothermic reactions', Journal of Mathematical Chemistry, vol. 55, pp. 1187 - 1201, http://dx.doi.org/10.1007/s10910-017-0733-0

Anderson C; Jovanoski Z; Sidhu H; Towers I, 2016, 'Logistic equation with a simple stochastic carrying capacity', ANZIAM Journal, vol. 56, pp. C431 - C445, http://dx.doi.org/10.0000/anziamj.v56i0.9386

Huang Z; Sidhu HS; Towers IN; Jovanoski Z; Gubernov VV, 2016, 'Nonadiabatic combustion waves in a two-step competitive exothermic-reaction model', Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal, vol. 57, pp. C14 - C31, http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/10391/0

Huang Z; Sidhu H; Towers I; Jovanoski Z; Gubernov V, 2015, 'Reaction waves in solid fuels for adiabatic competitive exothermic reactions', ANZIAM Journal, vol. 56, pp. C148 - C162, http://dx.doi.org/10.0000/anziamj.v56i0.9343

Towers IN; Jovanoski Z; Sidhu HS; Safuan H, 2015, 'On travelling wave solutions of the diffusive Leslie–Gower model', Applied Mathematics and Computation, vol. 274, pp. 362 - 371, http://dx.doi.org/10.1016/j.amc.2015.10.088

Safuan H; Sidhu H; Jovanoski Z; Towers I, 2014, 'A two-species predator-prey model in an environment enriched by a biotic resource', ANZIAM Journal, vol. 54, pp. C768 - C787, http://dx.doi.org/10.0000/anziamj.v54i0.6376

Sidhu H; Sharples J; Towers I; Gubernov V; wee W, 2013, 'Properties of reaction fronts in a non-adiabatic two stage exothermic-endothermic competitive reaction scheme', ANZIAM Journal, vol. 54, http://dx.doi.org/10.0000/anziamj.v54i0.6302

Towers I; Gubernov V; Kolobov AV; Polezhaev AA; Sidhu HS, 2013, 'Bistability of flame propagation in a model with competing exothermic reactions', Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences, vol. 469, pp. 20130315-1 - 20130315-19, http://dx.doi.org/10.1098/rspa.2013.0315

Jovanoski Z; Towers I; Sidhu HS; Mohd Safuan H, 2013, 'Exact solution of a non-autonomous logistic population model', Ecological Modelling, vol. 251, pp. 99 - 102, http://dx.doi.org/10.1016/j.ecolmodel.2012.12.016

Safuan H; Sidhu HS; Jovanoski Z; Towers I, 2013, 'Impacts of Biotic Resource Enrichment on a Predator-Prey Population', Bulletin of Mathematical Biology, vol. on-line July 2013, pp. 1798 - 1812, http://dx.doi.org/10.1007/s11538-013-9869-7

Towers I; Jovanoski Z; Sidhu HS; mohd safuan H, 2012, 'Coupled logistic carrying capacity model', The ANZIAM Journal, vol. 53, pp. C172 - C184, http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/4972

Towers I; Jovanoski Z, 2012, 'Shepherded solitons', The ANZIAM Journal, vol. 53, pp. C312 - C324, http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/5122

Konar S; Jovanoski Z; Towers I, 2011, 'Two-color bright solitons in a three-level atomic system in the cascade configuration', Journal of Modern Optics, vol. 58, pp. 1035 - 1040, http://dx.doi.org/10.1080/09500340.2011.591509

Konar S; Jovanoski Z; Towers I, 2011, 'Incoherent spatial optical solitons in photorefractive crystals', Optics and Laser Technology, vol. 43, pp. 1466 - 1469, http://dx.doi.org/10.1016/j.optlastec.2011.04.022

Oslington P; Towers I, 2010, 'Trade, Migration, and Inequality in a World without Factor Price Equalization', Review of International Economics, vol. 18, pp. 650 - 662, http://dx.doi.org/10.1111/j.1467-9396.2010.00902.x

Oslington PR; Towers I, 2009, 'Pushing Economies (and Students)Outside the Factor Price Equalization Zone', Journal of Economic Education, vol. 40, pp. 422 - 436, http://dx.doi.org/10.1080/00220480903238099

Towers I; Robinson G, 2009, 'A model for multiple isothermal circumstellar dust shells', Physica Scripta T, vol. 80, http://dx.doi.org/10.1088/0031-8949/80/01/015901

Robinson G; Towers I; Jovanoski Z, 2009, 'Isothermal circumstellar dust shell model for teaching', International Journal of Mathematical Education in Science and Technology, vol. 40, pp. 795 - 845, http://dx.doi.org/10.1080/00207390902825302

Towers I; Jovanoski Z, 2008, 'Application of rational Chebyshev polynomials to optical problems', The ANZIAM Journal, vol. 50, pp. C60 - C74

Jovanoski Z; Towers IN; Ansari NA, 2008, 'Domain walls and their stability', ANZIAM Journal, vol. 50

Jovanoski Z; Ansari NA; Towers I; Sammut RA, 2008, 'Exact domain-wall solitons', Physics Letters, Section A, vol. 372, pp. 610 - 612, http://dx.doi.org/10.1016/j.physleta.2007.07.068

Ansari NA; Towers I; Jovanoski Z; Sidhu HS, 2007, 'A semi-classical approach to two-frequency solitons in a three-level cascade atomic system', Optics Communications, vol. 274, pp. 66 - 73, http://dx.doi.org/10.1016/j.optcom.2007.02.019

Ansari NA; Jovanoski Z; Sidhu HS; Towers I, 2006, 'Non-Linear Interactions of Two Intense Fields with a Three-Level Atomic System', Journal of Nonlinear Optical Physics and Materials, vol. 15, pp. 401 - 414, http://dx.doi.org/10.1142/S0218863506003402

Towers I, 2005, 'Interrogating functions', International Journal of Mathematical Education in Science and Technology, vol. 36, pp. 922 - 930, http://dx.doi.org/10.1080/00207390500084948

Jovanoski Z; Towers I; Ansari NA; Sammut RA, 2005, 'Approximate analysis of circular bends in nonlinear planar waveguides', Optics Communications, vol. 244, pp. 399 - 409, http://dx.doi.org/10.1016/j.optcom.2004.09.036

Jovanoski Z; Towers I; Garth SJ; Sammut RA, 2005, 'Modes on a bent nonlinear waveguide: solutions based upon the method of perturbations', Journal of Modern Optics, vol. 52, pp. 707 - 723, http://dx.doi.org/10.1080/09500340412331283679

Towers IN; Malomed BA; Wise FW, 2003, 'Light bullets in quadratic media with normal dispersion at the second harmonic', PHYSICAL REVIEW LETTERS, vol. 90, http://dx.doi.org/10.1103/PhysRevLett.90.123902

Band YB; Towers I; Malomed BA, 2003, 'Unified semiclassical approximation for Bose-Einstein condensates: Application to a BEC in an optical potential', PHYSICAL REVIEW A, vol. 67, http://dx.doi.org/10.1103/PhysRevA.67.023602

Mihalache D; Mazilu D; Towers I; Malomed BA; Lederer F, 2003, 'Stable spatiiotemporal spinning solitons in a bimodal cubic-quintic medium', Physical Review E, vol. 67, pp. 566081 - 566089, http://dx.doi.org/10.1103/PhysRevE.67.056608

Mihalache D; Mazilu D; Towers I; Malomed BA; Lederer F, 2002, 'Stable two-dimensional spinning solitons in a bimodal cubic-quintic model with four-wave mixing', JOURNAL OF OPTICS A-PURE AND APPLIED OPTICS, vol. 4, pp. 615 - 623, http://dx.doi.org/10.1088/1464-4258/4/6/305

Towers IN; Malomed BA, 2002, 'Polychromatic solitons in a quadratic medium', PHYSICAL REVIEW E, vol. 66, http://dx.doi.org/10.1103/PhysRevE.66.046620

Mihalache D; Mazilu D; Crasovan L; Towers I; Buryak AV; Malomed BA; Torner L; Torres JP; Lederer F, 2002, 'Stable Spinning Optical Solitons in Three Dimensions', Physical Review Letters, vol. 88, pp. 1 - 4, http://dx.doi.org/10.1103/PhysRevLett.88.073902

Mihalache D; Mazilu D; Crasovan L; Towers I; Malomed BA; Buryak AV; Torner L; Lederer F, 2002, 'Stable three-dimensional spinning optical solitons supported by competing quadratic and cubic nonlinearities', Physical Review E, vol. 66, pp. 1 - 7, http://dx.doi.org/10.1103/PhysRevE.66.016613

Towers I; Malomed BA, 2002, 'Stable (2+1)-dimensional solitons in a layered medium with sign-alternating Kerr nonlinearity', Journal of the Optical Society of America B - Optical Physics, vol. 19, pp. 537 - 543, http://dx.doi.org/10.1364/JOSAB.19.000537

Elyutin PV; Buryak AV; Gubernov V; Sammut RA; Towers I, 2001, 'Interaction of two one-dimensional Bose-Einstein solitons: Chaos and energy exchange', Physical Review E, vol. 64, pp. 1 - 9, http://dx.doi.org/10.1103/PhysRevE.64.016607

Towers I; Buryak AV; Sammut RA; Malomed BA; Crasovan L; Mihalache D, 2001, 'Stability of spinning ring solitons of the cubic-quintic nonlinear Schrodinger equation', Physics Letters, Section A, vol. 288, pp. 292 - 298, http://dx.doi.org/10.1016/S0375-9601(01)00565-5

Towers I; Buryak AV; Sammut RA; Malomed BA, 2001, 'Stable localized vortex solitons', Physical Review E, vol. 63, pp. 1 - 4, http://dx.doi.org/10.1103/PhysRevE.63.055601

Malomed BA; Peng G; Chu PL; Towers I; Buryak AV; Sammut RA, 2001, 'Stable helical solitons in optical media', Pramana - Journal of Physics, vol. 57, pp. 1061 - 1078, http://dx.doi.org/10.1007/s12043-001-0014-z

Towers I; Buryak AV; Sammut RA; Malomed BA, 2000, 'Quadratic solitons resulting from double-resonance wave mixing', Journal of the Optical Society of America B - Optical Physics, vol. 17, pp. 2018 - 2025, http://dx.doi.org/10.1364/JOSAB.17.002018

Buryak AV; Towers I; Trillo S, 2000, 'Multistability, homoclinic clamping, and chaos in nonlinear quadratic distributied feedback systems', Physics Letters, Section A, vol. 267, pp. 319 - 325, http://dx.doi.org/10.1016/S0375-9601(00)00124-9

Towers I; Sammut RA; Buryak AV; Malomed BA, 1999, 'Soliton multistability as a result of double-resonance wave mixing in x(2) media', Optics Letters, vol. 24, pp. 1738 - 1740, https://www.ncbi.nlm.nih.gov/pubmed/18079920

Conference Papers

Sharples JJ; Gubernov VV; Sidhu HS; Towers IN; Kolobov AV; Polezhaev AA, 2020, 'Behaviour of combustion waves in one-step and two-step models', in 18th World IMACS Congress and MODSIM 2009 - International Congress on Modelling and Simulation: Interfacing Modelling and Simulation with Mathematical and Computational Sciences, Proceedings, pp. 4453 - 4459

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