ORCID Profile
0000-0001-6072-3102
Current Organisations
Queensland University of Technology
,
Wageningen University & Research
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Research Topics
In Research Link Australia (RLA), "Research Topics" refer to ANZSRC FOR and SEO codes. These topics are either sourced from ANZSRC FOR and SEO codes listed in researchers' related grants or generated by a large language model (LLM) based on their publications.
Top 5 Research Topics
ANZSRC Field of Research (FoR)
Dynamical Systems in Applications | Applied Mathematics | Partial Differential Equations | Biological Mathematics |
ANZSRC Socio-Economic Objective (SEO)
Expanding Knowledge in the Mathematical Sciences | Expanding Knowledge in the Biological Sciences
Related Links
Publications
Shock-fronted travelling waves in a reaction–diffusion model with nonlinear forward–backward–forward diffusion
Publisher: Elsevier BV
Date: 09-2021
A modified May–Holling–Tanner predator-prey model with multiple Allee effects on the prey and an alternative food source for the predator
Publisher: American Institute of Mathematical Sciences (AIMS)
Date: 2021
Cholesterol Regulation in Age-Related Macular Degeneration: A Framework for Mathematical Modelling of Drusen Biogenesis
Publisher: Springer Science and Business Media LLC
Date: 10-2020
A geometric construction of travelling wave solutions to the Keller--Segel model
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 29-08-2014
Bifurcations to travelling planar spots in a three-component FitzHugh–Nagumo system
Publisher: Elsevier BV
Date: 05-2014
Front Interactions in a Three-Component System
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2010
DOI: 10.1137/080744785
Numerical computation of an Evans function for travelling waves
Publisher: Elsevier BV
Date: 08-2015
DOI: 10.1016/J.MBS.2015.05.009
Abstract: We demonstrate a geometrically inspired technique for computing Evans functions for the linearised operators about travelling waves. Using the ex les of the F-KPP equation and a Keller-Segel model of bacterial chemotaxis, we produce an Evans function which is computable through several orders of magnitude in the spectral parameter and show how such a function can naturally be extended into the continuous spectrum. In both ex les, we use this function to numerically verify the absence of eigenvalues in a large region of the right half of the spectral plane. We also include a new proof of spectral stability in the appropriate weighted space of travelling waves of speed c≥2√δ in the F-KPP equation.
Turing patterns in a diffusive Holling–Tanner predator-prey model with an alternative food source for the predator
Publisher: Elsevier BV
Date: 08-2021
Spectral stability of travelling wave solutions in a Keller–Segel model
Publisher: Elsevier BV
Date: 07-2019
Pulse Dynamics in a Three-Component System: Existence Analysis
Publisher: Springer Science and Business Media LLC
Date: 05-09-2008
Butterfly Catastrophe for Fronts in a Three-Component Reaction–Diffusion System
Publisher: Springer Science and Business Media LLC
Date: 05-11-2014
Localized Patterns in a Three-Component FitzHugh–Nagumo Model Revisited Via an Action Functional
Publisher: Springer Science and Business Media LLC
Date: 25-10-2016
Novel solutions for a model of wound healing angiogenesis
Publisher: IOP Publishing
Date: 14-11-2014
Pulse dynamics in a three-component system: Stability and bifurcations
Publisher: Elsevier BV
Date: 12-2008
A Holling–Tanner Predator–Prey Model with Strong Allee Effect
Publisher: World Scientific Pub Co Pte Lt
Date: 10-2019
DOI: 10.1142/S0218127419300325
Abstract: We analyze a modified Holling–Tanner predator–prey model where the predation functional response is of Holling type II and we incorporate a strong Allee effect associated with the prey species production. The analysis complements the results of previous articles by Saez and González-Olivares [1999] and Arancibia-Ibarra and González-Olivares [2015] discussing Holling–Tanner models which incorporate a weak Allee effect. The extended model exhibits rich dynamics and we prove the existence of separatrices in the phase plane separating basins of attraction related to coexistence and extinction of the species. We also show the existence of a homoclinic curve that degenerates to form a limit cycle and discuss numerous potential bifurcations such as saddle-node, Hopf, and Bogdanov–Takens bifurcations.
Correction to: Pinned Solutions in a Heterogeneous Three-Component FitzHugh–Nagumo Model
Publisher: Springer Science and Business Media LLC
Date: 11-09-2018
Existence of traveling wave solutions for a model of tumor invasion
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2014
DOI: 10.1137/130923129
Pulse dynamics in reaction–diffusion equations with strong spatially localized impurities
Publisher: The Royal Society
Date: 05-03-2018
Abstract: In this article, a general geometric singular perturbation framework is developed to study the impact of strong, spatially localized, nonlinear impurities on the existence, stability and bifurcations of localized structures in systems of linear reaction–diffusion equations. By taking advantage of the multiple-scale nature of the problem, we derive algebraic conditions determining the existence and stability of pinned single- and multi-pulse solutions. Our methods enable us to explicitly control the spectrum associated with a (multi-)pulse solution. In the scalar case, we show how eigenvalues may move in and out of the essential spectrum and that Hopf bifurcations cannot occur. By contrast, even a pinned 1-pulse solution can undergo a Hopf bifurcation in a two-component system of linear reaction–diffusion equations with (only) one impurity. This article is part of the theme issue ‘Stability of nonlinear waves and patterns and related topics’.
Unfolding Symmetric Bogdanov–Takens Bifurcations for Front Dynamics in a Reaction–Diffusion System
Publisher: Springer Science and Business Media LLC
Date: 16-08-2019
A computational model for BMP movement in sea urchin embryos
Publisher: Elsevier BV
Date: 12-2014
DOI: 10.1016/J.JTBI.2014.08.026
Abstract: Bone morphogen proteins (BMPs) are distributed along a dorsal-ventral (DV) gradient in many developing embryos. The spatial distribution of this signaling ligand is critical for correct DV axis specification. In various species, BMP expression is spatially localized, and BMP gradient formation relies on BMP transport, which in turn requires interactions with the extracellular proteins Short gastrulation/Chordin (Chd) and Twisted gastrulation (Tsg). These binding interactions promote BMP movement and concomitantly inhibit BMP signaling. The protease Tolloid (Tld) cleaves Chd, which releases BMP from the complex and permits it to bind the BMP receptor and signal. In sea urchin embryos, BMP is produced in the ventral ectoderm, but signals in the dorsal ectoderm. The transport of BMP from the ventral ectoderm to the dorsal ectoderm in sea urchin embryos is not understood. Therefore, using information from a series of experiments, we adapt the mathematical model of Mizutani et al. (2005) and embed it as the reaction part of a one-dimensional reaction-diffusion model. We use it to study aspects of this transport process in sea urchin embryos. We demonstrate that the receptor-bound BMP concentration exhibits dorsally centered peaks of the same type as those observed experimentally when the ternary transport complex (Chd-Tsg-BMP) forms relatively quickly and BMP receptor binding is relatively slow. Similarly, dorsally centered peaks are created when the diffusivities of BMP, Chd, and Chd-Tsg are relatively low and that of Chd-Tsg-BMP is relatively high, and the model dynamics also suggest that Tld is a principal regulator of the system. At the end of this paper, we briefly compare the observed dynamics in the sea urchin model to a version that applies to the fly embryo, and we find that the same conditions can account for BMP transport in the two types of embryos only if Tld levels are reduced in sea urchin compared to fly.
Pinned fronts in heterogeneous media of jump type
Publisher: IOP Publishing
Date: 25-11-2010
Influences of Allee effects in the spreading of malignant tumours
Publisher: Elsevier BV
Date: 04-2016
DOI: 10.1016/J.JTBI.2015.12.024
Abstract: A recent study by Korolev et al. [Nat. Rev. Cancer, 14:371-379, 2014] evidences that the Allee effect-in its strong form, the requirement of a minimum density for cell growth-is important in the spreading of cancerous tumours. We present one of the first mathematical models of tumour invasion that incorporates the Allee effect. Based on analysis of the existence of travelling wave solutions to this model, we argue that it is an improvement on previous models of its kind. We show that, with the strong Allee effect, the model admits biologically relevant travelling wave solutions, with well-defined edges. Furthermore, we uncover an experimentally observed biphasic relationship between the invasion speed of the tumour and the background extracellular matrix density.
A generalized multilevel-hybrid chaotic oscillator for low-cost and power-efficient short-range chaotic communication systems
Publisher: Springer Science and Business Media LLC
Date: 22-01-2020
DOI: 10.1186/S13638-020-1644-5
Abstract: In this paper, we present and evaluate a novel multilevel hybrid-chaotic oscillator. The proposed generalized multilevel-hybrid chaotic oscillator (GM-HCO) was created by combining a multilevel discrete function generated from user data with a continuous function having a d ing factor greater than l n (2) to achieve variable rates and adaptive carrier frequencies. Improved spectral efficiency and lower complexity of the transceiver compared with differentially coherent systems were achieved by multilevel signals at the transmitter and a matched filter at the receiver. An exact analytical solution for the generalized fixed basis function and the impulse response of the matched filter were also derived. The bit error rate (BER) expression of the GM-HCO was derived for two levels. It was found that the noise performance of the proposed system was better than a hybrid chaotic system based on forward time and differential chaos shift keying (DCSK). A comprehensive set of simulations were carried out to evaluate the performance of the proposed system with chaotic communication systems in the presence of additive white Gaussian noise (AWGN). The performance of the proposed system was comparable with that of conventional communication systems. The results demonstrate that the proposed system can offer better noise performance than existing chaotic communication systems, and it also offers variable transmitter frequencies and improved spectral efficiency. Noise-like behavior of the chaotic signals provides an additional layer of security at the physical layer compared with conventional (sinusoidal) communication systems.
(In)stability of Travelling Waves in a Model of Haptotaxis
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2020
DOI: 10.1137/19M1259705
Pinned Solutions in a Heterogeneous Three-Component FitzHugh–Nagumo Model
Publisher: Springer Science and Business Media LLC
Date: 11-08-2018
Seaweed cultivation and the remediation of by-products from ethanol production: a glorious green growth
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 25-05-2016
Planar Radial Spots in a Three-Component FitzHugh–Nagumo System
Publisher: Springer Science and Business Media LLC
Date: 10-05-2011
A Geometric Approach to Stationary Defect Solutions in One Space Dimension
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2016
DOI: 10.1137/15M1026742
Related Organisations
Related Funding Activities
A Novel Geometric Approach To Shocks In Reaction-Nonlinear Diffusion Models
Start Date: 2020
End Date: 2022
Funder: Australian Research Council
View Funded ActivityNew Mathematics For Understanding Complex Patterns In The Natural Sciences
Start Date: 2019
End Date: 2021
Funder: Australian Research Council
View Funded ActivityDiscovery Projects - Grant ID: DP190102545
Start Date: 07-2019
End Date: 12-2023
Amount: $406,000.00
Funder: Australian Research Council
View Funded ActivityDiscovery Projects - Grant ID: DP200102130
Start Date: 03-2020
End Date: 08-2024
Amount: $480,000.00
Funder: Australian Research Council
View Funded ActivityDiscovery Early Career Researcher Award - Grant ID: DE140100741
Start Date: 03-2014
End Date: 06-2018
Amount: $389,564.00
Funder: Australian Research Council
View Funded Activity