ORCID Profile
0000-0001-9888-944X
Current Organisation
Monash University
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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 | Pure Mathematics | Ordinary Differential Equations, Difference Equations and Dynamical Systems | Numerical and Computational Mathematics not elsewhere classified
ANZSRC Socio-Economic Objective (SEO)
Related Links
Publications
A computer-assisted proof of the existence of traveling wave solutions to the scalar Euler equations with artificial viscosity
Publisher: Springer Science and Business Media LLC
Date: 02-06-2011
Enclosing all zeros of a system of analytic functions
Publisher: Elsevier BV
Date: 05-2019
Reconstructing Metabolic Networks Using Interval Analysis
Publisher: Springer Berlin Heidelberg
Date: 2005
DOI: 10.1007/11557067_16
A rigorous lower bound for the stability regions of the quadratic map
Publisher: Elsevier BV
Date: 09-2009
Is the Hénon attractor chaotic?
Publisher: AIP Publishing
Date: 03-2015
DOI: 10.1063/1.4913945
Abstract: By performing a systematic study of the Hénon map, we find low-period sinks for parameter values extremely close to the classical ones. This raises the question whether or not the well-known Hénon attractor—the attractor of the Hénon map existing for the classical parameter values—is a strange attractor, or simply a stable periodic orbit. Using results from our study, we conclude that even if the latter were true, it would be practically impossible to establish this by computing trajectories of the map.
Combination of exhaustive search and continuation method for the study of sinks in the Hénon map
Publisher: IEEE
Date: 05-2013
A Note on the Convergence of Parametrised Non-Resonant Invariant Manifolds
Publisher: Springer Science and Business Media LLC
Date: 02-02-2011
Interval analysis techniques for boundary value problems of elasticity in two dimensions
Publisher: Elsevier BV
Date: 02-2007
There and back again: Split and prune to tighten
Publisher: IEEE
Date: 07-2013
Automated computation of robust normal forms of planar analytic vector fields
Publisher: American Institute of Mathematical Sciences (AIMS)
Date: 2009
Short periodic orbits for the Lorenz system
Publisher: IEEE
Date: 2008
Optimal Design in Population Kinetic Experiments by Set-Valued Methods
Publisher: Springer Science and Business Media LLC
Date: 15-07-2011
Computer-assisted techniques for the verification of the Chebyshev property of Abelian integrals
Publisher: Elsevier BV
Date: 04-2013
Rigorous parameter reconstruction for differential equations with noisy data
Publisher: Elsevier BV
Date: 09-2008
A Rigorous ODE Solver and Smale’s 14th Problem
Publisher: Springer Science and Business Media LLC
Date: 2002
The Lorenz attractor exists
Publisher: Elsevier BV
Date: 06-1999
Invertibility Properties of Singular Integral Operators Associated with the Lamé and Stokes Systems on Infinite Sectors in Two Dimensions
Publisher: Springer Science and Business Media LLC
Date: 24-08-2017
A rigorous study of possible configurations of limit cycles bifurcating from a hyper-elliptic Hamiltonian of degree five
Publisher: Informa UK Limited
Date: 27-04-2009
Estimating parameters for generalized mass action models using constraint propagation
Publisher: Elsevier BV
Date: 08-2007
DOI: 10.1016/J.MBS.2006.11.009
Abstract: As modern molecular biology moves towards the analysis of biological systems as opposed to their in idual components, the need for appropriate mathematical and computational techniques for understanding the dynamics and structure of such systems is becoming more pressing. For ex le, the modeling of biochemical systems using ordinary differential equations (ODEs) based on high-throughput, time-dense profiles is becoming more common-place, which is necessitating the development of improved techniques to estimate model parameters from such data. Due to the high dimensionality of this estimation problem, straight-forward optimization strategies rarely produce correct parameter values, and hence current methods tend to utilize genetic/evolutionary algorithms to perform non-linear parameter fitting. Here, we describe a completely deterministic approach, which is based on interval analysis. This allows us to examine entire sets of parameters, and thus to exhaust the global search within a finite number of steps. In particular, we show how our method may be applied to a generic class of ODEs used for modeling biochemical systems called Generalized Mass Action Models (GMAs). In addition, we show that for GMAs our method is amenable to the technique in interval arithmetic called constraint propagation, which allows great improvement of its efficiency. To illustrate the applicability of our method we apply it to some networks of biochemical reactions appearing in the literature, showing in particular that, in addition to estimating system parameters in the absence of noise, our method may also be used to recover the topology of these networks.
A computer-assisted proof of the existence of solutions to a boundary value problem with an integral boundary condition
Publisher: Elsevier BV
Date: 03-2011
On the global stability of a peer-to-peer network model
Publisher: Elsevier BV
Date: 05-2012
NUMERICAL STUDY OF COEXISTING ATTRACTORS FOR THE HÉNON MAP
Publisher: World Scientific Pub Co Pte Lt
Date: 07-2013
DOI: 10.1142/S0218127413300255
Abstract: The question of coexisting attractors for the Hénon map is studied numerically by performing an exhaustive search in the parameter space. As a result, several parameter values for which more than two attractors coexist are found. Using tools from interval analysis, we show rigorously that the attractors exist. In the case of periodic orbits, we verify that they are stable, and thus proper sinks. Regions of existence in parameter space of the found sinks are located using a continuation method the basins of attraction are found numerically.
Parameter Reconstruction for Biochemical Networks Using Interval Analysis
Publisher: Springer Science and Business Media LLC
Date: 29-07-2006
CAMPARY: Cuda Multiple Precision Arithmetic Library and Applications
Publisher: Springer International Publishing
Date: 2016
Enclosing all zeros of an analytic function — A rigorous approach
Publisher: Elsevier BV
Date: 06-2009
Non-uniformly expanding dynamics in maps with singularities and criticalities
Publisher: Springer Science and Business Media LLC
Date: 12-1999
DOI: 10.1007/BF02698857
Fundamentals of Chaos
Publisher: Springer Berlin Heidelberg
Date: 2009
On a computer-aided approach to the computation of Abelian integrals
Publisher: Springer Science and Business Media LLC
Date: 15-02-2011
Computing accurate Poincaré maps
Publisher: Elsevier BV
Date: 10-2002
On the Existence of the Double Scroll Attractor for the Chua's Circuit with a Smooth Nonlinearity
Publisher: IEEE
Date: 2018
S-system parameter estimation for noisy metabolic profiles using Newton-flow analysis
Publisher: Institution of Engineering and Technology (IET)
Date: 05-2007
Abstract: Biochemical systems are commonly modelled by systems of ordinary differential equations (ODEs). A particular class of such models called S-systems have recently gained popularity in biochemical system modelling. The parameters of an S-system are usually estimated from time-course profiles. However, finding these estimates is a difficult computational problem. Moreover, although several methods have been recently proposed to solve this problem for ideal profiles, relatively little progress has been reported for noisy profiles. We describe a special feature of a Newton-flow optimisation problem associated with S-system parameter estimation. This enables us to significantly reduce the search space, and also lends itself to parameter estimation for noisy data. We illustrate the applicability of our method by applying it to noisy time-course data synthetically produced from previously published 4- and 30-dimensional S-systems. In addition, we propose an extension of our method that allows the detection of network topologies for small S-systems. We introduce a new method for estimating S-system parameters from time-course profiles. We show that the performance of this method compares favorably with competing methods for ideal profiles, and that it also allows the determination of parameters for noisy profiles.
Robust normal forms for saddles of analytic vector fields
Publisher: IOP Publishing
Date: 28-07-2004
The Songling system has exactly four limit cycles
Publisher: Elsevier BV
Date: 02-2022
Rigorous study of short periodic orbits for the Lorenz system
Publisher: IEEE
Date: 05-2008
A database of rigorous and high-precision periodic orbits of the Lorenz model
Publisher: Elsevier BV
Date: 09-2015
Interval Methods
Publisher: Springer International Publishing
Date: 27-10-2015
VALIDATED STUDY OF THE EXISTENCE OF SHORT CYCLES FOR CHAOTIC SYSTEMS USING SYMBOLIC DYNAMICS AND INTERVAL TOOLS
Publisher: World Scientific Pub Co Pte Lt
Date: 02-2011
DOI: 10.1142/S021812741102857X
Abstract: We show that, for a certain class of systems, the problem of establishing the existence of periodic orbits can be successfully studied by a symbolic dynamics approach combined with interval methods. Symbolic dynamics is used to find approximate positions of periodic points, and the existence of periodic orbits in a neighborhood of these approximations is proved using an interval operator. As an ex le, the Lorenz system is studied a theoretical argument is used to prove that each periodic orbit has a distinct symbol sequence. All periodic orbits with the period p ≤ 16 of the Poincaré map associated with the Lorenz system are found. Estimates of the topological entropy of the Poincaré map and the flow, based on the number and flow-times of short periodic orbits, are calculated. Finally, we establish the existence of several long periodic orbits with specific symbol sequences.
Symbolic dynamics based method for rigorous study of the existence of short cycles for chaotic systems
Publisher: IEEE
Date: 05-2009
Fixed points of a destabilized Kuramoto–Sivashinsky equation
Publisher: Elsevier BV
Date: 09-2015
AN IMPROVED LOWER BOUND ON THE NUMBER OF LIMIT CYCLES BIFURCATING FROM A QUINTIC HAMILTONIAN PLANAR VECTOR FIELD UNDER QUINTIC PERTURBATION
Publisher: World Scientific Pub Co Pte Lt
Date: 2010
DOI: 10.1142/S0218127410025405
Abstract: The limit cycle bifurcation of a Z 2 equivariant quintic planar Hamiltonian vector field under Z 2 equivariant quintic perturbation is studied. We prove that the given system can have at least 27 limit cycles. This is an improved lower bound on the possible number of limit cycles that can bifurcate from a quintic planar Hamiltonian system under quintic perturbation.
Rigorous integration of smooth vector fields around spiral saddles with an application to the cubic Chua's attractor
Publisher: Elsevier BV
Date: 02-2019
AN IMPROVED LOWER BOUND ON THE NUMBER OF LIMIT CYCLES BIFURCATING FROM A HAMILTONIAN PLANAR VECTOR FIELD OF DEGREE 7
Publisher: World Scientific Pub Co Pte Lt
Date: 05-2010
DOI: 10.1142/S0218127410026599
Abstract: The limit cycle bifurcations of a Z 2 equivariant planar Hamiltonian vector field of degree 7 under Z 2 equivariant degree 7 perturbation is studied. We prove that the given system can have at least 53 limit cycles. This is an improved lower bound for the weak formulation of Hilbert's 16th problem for degree 7, i.e. on the possible number of limit cycles that can bifurcate from a degree 7 planar Hamiltonian system under degree 7 perturbation.
Related Organisations
Related Funding Activities
Discovery Projects - Grant ID: DP220100492
Start Date: 07-2022
End Date: 06-2025
Amount: $400,000.00
Funder: Australian Research Council
View Funded Activity