College of Sciences staff

Dr Alona Ben-Tal staff profile picture

Contact details +64 (09) 414 0800  ext. 43608

Dr Alona Ben-Tal PhD (Auckland), Msc (Technion)

Senior Lecturer

Institute of Natural and Mathematical Sciences

My main area of research in recent years has been the cardio-respiratory system of mammals. I have developed simplified models of lung mechanics, gas exchange and neural control of breathing and studied different aspects of the integrated system. I have also studied the interactions between the heart and the lungs and contributed to a study of optimal nutritional intake of pregnant sheep and modelling high speed weighing systems.



  • PhD in Mathematics - Auckland (2001)
  • Msc in Mechanical Engineering - Technion Israel Institute of Technology (1994)
  • Bsc (Cum Laude) in Mechanical Engineering - Technion Israel Institute of Technology (1990)

Prizes and Awards

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): Biological Mathematics (010202): Dynamical Systems in Applications (010204): Mathematical Sciences (010000): Numerical and Computational Mathematics (010300)

Research Projects

Summary of Research Projects

Position Current Completed
Project Leader 1 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.
Read Project Description Hide Project Description

Date Range: 2009 - 2012

Funding Body: Marsden Fund - Full

Project Team:

Project Title: A mechanism for Chayne-Stokes respiration

Date Range: 2006 - 2008

Funding Body: Royal Society of New Zealand

Project Team:

Research Outputs


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.
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., 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., 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., Wake, G.
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.
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., Wake, G.
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. (2017, August). Mathematical modelling of the cardiorespiratory system. Presented at IUPS 2017. Rio de Janeiro, Brazil.
[Conference Oral Presentation]Authored by: Ben-Tal, A.
Elbeltagi, R., Ben-Tal, A., Potgieter, J., & Chang, JY. (2011). In-process weighing systems. ASME 2011 International Mechanical Engineering Congress and Exposition, IMECE 2011. Vol. 7 (pp. 1113 - 1122).
[Conference Paper in Published Proceedings]Authored by: Ben-Tal, A., Potgieter, J.

Supervision and Teaching

Summary of Doctoral Supervision

Position Current Completed
Supervisor 2 0


Papers taught recently:

160.203 Calculus.

160.319 Mathematical Modelling.

160.715 Advanced Computational Methods.

Current Doctoral Supervision

Supervisor of:

  • Shumaila Noreen - PhD
    The effect of Respiratory Sinus Arrhythmia on coronary blood flow and cardiac output
  • Syed Zaidi - PhD
    Control of respiration and the work of breathing

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