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Associate Professor Alona Ben-Tal staff profile picture

Contact details +6492136608

Associate Professor Alona Ben-Tal MSc, BSc, PhD, NZMS

Associate Professor/Deputy Head of School

Doctoral Supervisor
School of Natural and Computational Sciences

My research is truly interdisciplinary and lies in the fields of applied mathematics, dynamical systems, numerical methods and physiology. My main interest is the integrated behaviour of the cardiorespiratory system and over the years, I have studied different aspects of this system including lung mechanics, gas exchange, neural control of breathing and heart rate control. My research involves mathematical modelling at different levels of complexity and mathematical analysis using a variety of mathematical techniques. 



  • Master of Science - Israel Institute of Technology (1994)
  • Bachelor of Science - Israel Institute of Technology (1991)
  • Doctor of Philosophy - University of Auckland (2001)

Fellowships and Memberships

  • Member, New Zealand Mathematical Society (Fellow) (2016)

Certifications and Registrations

  • Licence, Supervisor, Massey University

Research Expertise

Research Interests

Dynamical systems.

Mathematical modelling.

Numerical methods.

Regulation and function of the cardio-respiratory system.


Health and Well-being

Area of Expertise

Field of research codes
Applied Mathematics (010200):
Curriculum and Pedagogy (130200): Education (130000): Education Systems (130100):
Engineering (090000):
Higher Education (130103):
Interdisciplinary Engineering (091500):
Mathematical Sciences (010000):
Medical And Health Sciences (110000): Medical Physiology (111600):
Numerical and Computational Mathematics (010300):
Science, Technology and Engineering Curriculum and Pedagogy (130212):
Systems Physiology (111603)


Mathematical Biology and Modelling

Applied Mathematics

Industrial Mathematics

Research Projects

Summary of Research Projects

Position Current Completed
Project Leader 3 3
Team Member 0 1

Completed Projects

Project Title: Complexity reduction in neural models

Mathematical models of biological systems provide understanding and predictive power. However, as more information about a particular system is collected, its model becomes increasingly complicated. This makes the models better, because they are becoming more realistic and therefore potentially more useful, but in turn they are becoming harder to simulate and analyse. The aim of this research is to overcome this problem by using recently-developed, so-called 'equation-free' techniques for the study of complex systems, concentrating on a variety of model neural networks. In particular we will study the respiratory neural system. This complex system regulates breathing by sending electrical signals to the diaphragm and other respiratory muscles, causing them to periodically contract and relax. Equation-free techniques allow one to automatically simplify a complex system such as the respiratory neural network by using judiciously designed computer simulations to capture the 'essence' of the original complex system in terms of the correct variables. This provides insights and understanding that cannot be found in any other way.
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Date Range: 2009 - 2012

Funding Body: Marsden Fund - Full

Project Team:

Research Outputs


Zaidi, F., Ben-Tal, A., & Roberts, M. (2021). Is our breathing optimal? Solving a piecewise linear model with constraints. Journal of Mathematical Biology. 83(4)
[Journal article]Authored by: Ben-Tal, A., Roberts, M.
Ben-Tal, A., Wang, Y., & Leite, MCA. (2019). The logic behind neural control of breathing pattern. Scientific Reports. 9(1)
[Journal article]Authored by: Ben-Tal, A.
Ben-Tal, A. (2018). Mathematical Modelling Disproves Decades-old Hypothesis, a Potential New Way to Treat Heart Disease.. SIAM news.
[Journal article]Authored by: Ben-Tal, A.
Ben-Tal, A., & Kevrekidis, IG. (2016). Coarse-graining and simplification of the dynamics seen in bursting neurons. SIAM Journal on Applied Dynamical Systems. 15(2), 1193-1226
[Journal article]Authored by: Ben-Tal, A.
Elstad, M., O’Callaghan, EL., Smith, AJ., Ben-Tal, A., & Ramchandra, R. (2018). Cardiorespiratory interactions in humans and animals: Rhythms for life. American Journal of Physiology - Heart and Circulatory Physiology. 315(1), H6-H17
[Journal article]Authored by: Ben-Tal, A.
Harvey, EP., & Ben-Tal, A. (2016). Robust Unidirectional Airflow through Avian Lungs: New Insights from a Piecewise Linear Mathematical Model. PLoS Computational Biology. 12(2)
[Journal article]Authored by: Ben-Tal, A.
Molkov, YI., Shevtsova, NA., Park, C., Ben-Tal, A., Smith, JC., Rubin, JE., . . . Rybak, IA. (2014). A closed-loop model of the respiratory system: Focus on hypercapnia and active expiration. PLoS ONE. 9(10)
[Journal article]Authored by: Ben-Tal, A.
Ben-Tal, A., Shamailov, SS., & Paton, JFR. (2014). Central regulation of heart rate and the appearance of respiratory sinus arrhythmia: New insights from mathematical modeling. Mathematical Biosciences. 255(1), 71-82
[Journal article]Authored by: Ben-Tal, A.
Ben-Tal, A., & Tawhai, MH. (2013). Integrative approaches for modeling regulation and function of the respiratory system. Wiley Interdisciplinary Reviews: Systems Biology and Medicine. 5(6), 687-699
[Journal article]Authored by: Ben-Tal, A.
Ben-Tal, A., Shamailov, SS., & Paton, JFR. (2012). Evaluating the physiological significance of respiratory sinus arrhythmia: Looking beyond ventilation-perfusion efficiency. Journal of Physiology. 590(8), 1989-2008
[Journal article]Authored by: Ben-Tal, A.
Ben-Tal, A. (2012). Computational models for the study of heart-lung interactions in mammals. Wiley Interdisciplinary Reviews: Systems Biology and Medicine. 4(2), 163-170
[Journal article]Authored by: Ben-Tal, A.
Kiataramkul, C., Wake, GC., Ben-Tal, A., & Lenbury, Y. (2011). Optimal nutritional intake for fetal growth. Mathematical Biosciences and Engineering. 8(3), 723-732
[Journal article]Authored by: Ben-Tal, A.
Ben-Tal, A., & Smith, JC. (2010). Control of breathing: Two types of delays studied in an integrated model of the respiratory system. Respiratory Physiology and Neurobiology. 170(1), 103-112
[Journal article]Authored by: Ben-Tal, A.
Ben-Tal, A., & Smith, JC. (2008). A model for control of breathing in mammals: Coupling neural dynamics to peripheral gas exchange and transport. Journal of Theoretical Biology. 251(3), 480-497
[Journal article]Authored by: Ben-Tal, A.
Ben-Tal, A. (2006). Simplified models for gas exchange in the human lungs. Journal of Theoretical Biology. 238(2), 474-495
[Journal article]Authored by: Ben-Tal, A.
(2002). Symmetry restoration in a class of forced oscillators. Physica D: Nonlinear Phenomena. 171(4), 236-248
[Journal article]Authored by: Ben-Tal, A.
Ben-Tal, A., Kirk, V., & Wake, G. (2001). Banded chaos in power systems. IEEE Transactions on Power Delivery. 16(1), 105-110
[Journal article]Authored by: Ben-Tal, A.
Ben-Tal, A., Shein, D., & Zissu, S. (1999). Studying ferroresonance in actual power systems by bifurcation diagram. Electric Power Systems Research. 49(3), 175-183
[Journal article]Authored by: Ben-Tal, A.
Ben-Tal, A., Bar-Yoseph, PZ., & Flashner, H. (1996). Space-time spectral element method for optimal slewing of a flexible beam. International Journal for Numerical Methods in Engineering. 39(18), 3101-3121
[Journal article]Authored by: Ben-Tal, A.
Ben-Tal, A., Bar-Yoseph, P., & Flashner, H. (1995). Optimal maneuver of a flexible arm by space-time finite element method. Journal of Guidance, Control, and Dynamics. 18(6), 1459-1462
[Journal article]Authored by: Ben-Tal, A.


Ben-Tal, A. (2021). Useful Transformations from Non-autonomous to Autonomous Systems. In Understanding Complex Systems. (pp. 163 - 174).
[Chapter]Authored by: Ben-Tal, A.

Teaching and Supervision

Teaching Statement

Papers taught recently:

160.203 Calculus.

160.319 Mathematical Modelling.

160.715 Advanced Computational Methods.

Courses Coordinated

Summary of Doctoral Supervision

Position Current Completed
Main Supervisor 2 1
Co-supervisor 1 0

Current Doctoral Supervision

Main Supervisor of:

  • Shumaila Noreen - Doctor of Philosophy
    Mathematical modelling of the cardiovascular system to study the effects of respiratory sinus arrhythmia and heart failure.
  • Sidra Zafar - Doctor of Philosophy
    Equation-free investigations of heterogeneous networks.

Co-supervisor of:

  • Neelum Bashir - Doctor of Philosophy
    Computational Studies in the Planar Symmetric Few-Body Problem

Completed Doctoral Supervision

Main Supervisor of:

  • 2019 - Syed Zaidi - Doctor of Philosophy