The project idea is to use mathematical modelling, analysis and system identification tools of dynamic systems for discerning, quantification, and explanation of endocrine control mechanisms.
This is a long-term cooperation project between Uppsala University and Russian researchers residing both in Russia and other countries, initiated with seed funding from the Royal Swedish Academy of Science. Further on, the project was supported by EdG from European Research Council, and multiple grants from the Swedish Research Council.

• Researchers at UU: Alexander Medvedev
• Researchers at Saint Petersburg State University: Alexander Churilov, Alexander Shepeljavyi
• Researcher at Southwest State University (Russia): Zhanybai Zhusubaliev
• Researcher at TU Delft: Anton Proskurnikov

Graduated PhD students at UU: Diana, Yamalova, Per Mattsson, Egi Hidayat

• The mathematical model of the impulsive Goodwin's oscillator has been proposed to portray pulsatile endocrine regulation
• The model has been shown to agree well with endocrine data of testosterone regulation in the human male
• Under periodic exogenous excitation, the model has been demonstrated to exhibit bistability controlled by the phase of the exogenous signal. The discovered phenomenon offers an explanation to the changes in the endocrine system due to jet lag.

PhD Theses

• Diana Yamalova, Hybrid observers for systems withintrinsic pulse-modulated feedback
• Per Mattsson, Modeling and identification of nonlinear and impulsive systems
• Egi Hidayat, On Identification of Biological Systems

Licentiate Theses

• Diana Yamalova, Hybrid observers for systems with intrinsic pulse-modulated feedback
• Per Mattsson, Pulse-modulated feedback in mathematical modeling and estimation of endocrine systems
• Egi Hidayat, On Identification of Endocrine Systems

Journal Papers

• A. Medvedev, P. Mattsson, Zh. Zhusubaliyev, and V. Avrutin "Nonlinear dynamics and entrainment in a continuously forced pulse-modulated model of testosterone regulation", Nonlinear Dynamics, (), 1-17, 2018.
• A. Churilov, A. Medvedev, and Zh. Zhusubaliyev "Discrete-time Mapping for an Impulsive Goodwin Oscillator with Three Delays", International Journal of Bifurcation and Chaos, 27, 1750182, 2017.
• A. Churilov and A. Medvedev "Discrete-time map for an impulsive Goodwin oscillator with a distributed delay", Mathematics of Control, Signals, and Systems, March 2016, 28:9.
• D. Yamalova, A. Churilov, and A. Medvedev "Finite-dimensional Hybrid Observer for Delayed Impulsive Model of Testosterone Regulation", Mathematical Problems in Engineering, Vol. 2015 (2015), Article ID 190463
• Zh. Zhusubaliyev, E. Mosekilde, A. Churilov, and A. Medvedev "Multistability and Hidden Attractors in an Impulsive Goodwin Oscillator with Time Delay", The European Physical Journal Special Topics, July 2015, Volume 224, Issue 8, pp 1519-1539.
• A. Churilov, A. Medvedev, and Zh. Zhusubaliyev "Impulsive Goodwin Oscillator with Large Delay: Periodic Oscillations, Bistability, and Attractors" Nonlinear Analysis: Hybrid Systems, Vol. 21, August 2016, pp. 171-183.
• A. Churilov, A. Medvedev "An impulse-to-impulse discrete-time mapping for a time-delay impulsive system", Automatica, v. 50, no. 8, August 2014, pp. 2187-2190.
• A. Churilov, A. Medvedev, P. Mattsson "Periodical Solutions in a Pulse-Modulated Model of Endocrine Regulation with Time-Delay", IEEE Transactions on Automatic Control, v. 59, no. 3, March 2014, pp. 728-733
• E. Hidayat, A. Medvedev," Laguerre domain identification of continuous linear time delay systems from impulse response data", Automatica, V. 48, no. 11, November 2012, pp. 2902-2907
• Zh. Zhusubaliyev, A. Churilov and A. Medvedev "Bifurcation Phenomena in an Impulsive Model of Non-basal Testosterone Regulation", Chaos: An Interdisciplinary Journal of Nonlinear Science, 22, 013121 (2012)
• A. Churilov, A. Medvedev, A. Shepeljavyi, "State observer for continuous oscillating systems under intrinsic pulse-modulated feedback", Automatica, September, 2011
• A. Churilov, A. Medvedev, A. Shepeljavyi, "Mathematical model of non-basal testosterone regulation in the male by pulse modulated feedback", Automatica, v. 45, 2009, pp. 78-85.
• A. Medvedev, A. Churilov, and A. Shepeljavyi, "Mathematical models of testosterone regulation," in Stochastic optimization in informatics (in Russian). Saint Petersburg State University, 2006, no. 2, pp. 147-158.

Book Chapters

• A. Churilov, A. Medvedev, and Zh. Zhusubaliyev, "Complex dynamics and hidden attractors in a system of impulsive differential equations with an arbitrary constant delay", accepted for publication in "Multistability and Hidden Attractors in Nonlinear Dynamical Systems", 2017.
• P. Mattsson and A. Medvedev, "Modeling of testosterone regulation by pulse-modulated feedback", in Adv Exp Med Biol. 2015;823:23-40., Springer.

Conference Papers

• D. Yamalova, A. Medvedev, "Robustification of the Synchronous Mode in a Hybrid Observer for a Continuous System under an Intrinsic Pulse-modulated Feedback", 2018 European Control Conference, Limassol, Cyprus.
• A. Medvedev, A. Proskurnikov, and Zh. Zhusubaliev, "Entrainment in harmonically forced continuous and impulsive Goodwin's oscillators: a comparison study", 2018 European Control Conference, Limassol, Cyprus.
• D. Yamalova, A. Medvedev, "Hybrid Observers for an Impulsive Goodwin's Oscillator Subject to Continuous Exogenous Signals", 56th IEEE Conference on Decision and Control, Melbourne, Australia, 2017.
• D. Yamalova, A. Churilov, A. Medvedev, "Hybrid Observer for an Intrinsic Impulsive Feedback System", 20th IFAC World Congress, Toulouse, France, 2017.
• D. Yamalova, A. Medvedev, "Design of a Hybrid Observer for an Oscillator with an Intrinsic Pulse-Modulated Feedback", 2017 American Control Conference, Seattle, WA.
• P. Mattsson, A. Medvedev, Zh. Zhusubaliev, "Pulse-Modulated Model of Testosterone Regulation Subject to Exogenous Signals", 55th IEEE Conference on Decision and Control, Las Vegas, Nevada, 2016
• A. Churilov, A. Medvedev, Zh. Zhusubaliyev "Delay-induced Dynamical Phenomena in Impulsive Goodwin's Oscillator: What We Know So Far", Invited Session: Biological Oscillators, 54th IEEE Conference on Decision and Control, Osaka, Japan, 2015
• D. Yamalova, A. Churilov, A. Medvedev "State Estimation in a Delayed Impulsive Model of Testosterone Regulation by a Finite-dimensional Hybrid Observer", European Control Conference, Linz, Austria, July, 2015
• D. Yamalova, A. Churilov, A. Medvedev "Design Degrees of Freedom in a Hybrid Observer for a Continuous Plant under an Intrinsic Pulse-modulated Feedback", 1st IFAC Conference on Modelling, Identification and Control of Nonlinear Systems, Saint Petersburg, Russia, June, 2015
• A. Churilov, A. Medvedev, P. Mattsson "Discrete-time Modeling of a Hereditary Impulsive Feedback System", 53rd IEEE Conference on Decision and Control, December 15-17, 2014, Los Angeles, California, USA.
• D. Yamalova, A. Churilov, and A. Medvedev "Hybrid State Observer for Time-Delay Systems under Intrinsic Impulsive Feedback", 21st International Symposium on Mathematical Theory of Networks and Systems, Groningen Netherlands, July, 2014
• A. Churilov, A. Medvedev, Zh. Zhusubaliyev, "Periodic Modes and Bistability in an Impulsive Goodwin Oscillator with Large Delay", IFAC World Congress, August 2014, Cape Town, South Africa
• P. Mattsson and T. Wigren, "Recursive Identification of Hammerstein Models from Small Data Sets", accepted for presentation at American Control Conference (ACC), June 2014, Portland, USA.
• P. Mattsson and A. Medvedev, "Modeling of testosterone regulation by pulse-modulated feedback: an experimental study", International Symposium on Computational Models for Life Sciences, November 2013, Sydney, Australia.
• A. Churilov, A. Medvedev, P. Mattsson, "On Finite-dimensional Reducibility of Time-delay Systems under Pulse-modulated Feedback", 52nd IEEE Conference on Decision and Control, Firenze, Italy, December, 2013.
• D. Yamalova, A. Churilov and A. Medvedev, "Hybrid State Observer with Modulated Correction for Periodic Systems under Intrinsic Impulsive Feedback", 5th IFAC International Workshop on Periodic Control Systems, Caen, France, July, 2013.
• A. Churilov, A. Medvedev and Zh. Zhusubaliyev, "Conditional Stability of a State Observer for a Hybrid Plant with a First-order Continuous Dynamics" 5th IFAC International Workshop on Periodic Control Systems, Caen, France, July, 2013.
• A. Churilov, A. Medvedev, Zh. Zhusubaliev, "State observer for a first-order plant under intrinsic pulse-modulated feedback: a case study", European Control Conference, Zurich, Switzerland, July 17-19, 2013.
• P. Mattsson, A. Medvedev "State Estimation in Linear Time-Invariant Systems With Unknown Impulsive Inputs", European Control Conference, Zurich, Switzerland, July 17-19, 2013.
• A. Churilov, A. Medvedev and P. Mattsson, "Periodical Solutions in a Time-delay Model of Endocrine Regulation by Pulse-modulated Feedback", 51st IEEE Conference on Decision and Control, December 2012, Maui, USA.
• A. Medvedev, "Discrete-continuous Mathematical Modeling of Endocrine Systems with Pulsatile Secretion", VPH2012: Integrative Approaches to Computational Biomedicine, September, 2012, London, UK.
• E. Hidayat and A. Medvedev, "Identification of a Pulsatile Endocrine Model from Hormone Concentration Data", the 2012 IEEE Multi-conference on Systems and Control, Dubrovnik, Croatia, October, 2012.
• E. Hidayat and A. Medvedev, "Continuous time delay estimation in Laguerre domain - Revisited", 16th IFAC Symposium on System Identification (SYSID 2012), Brussels, Belgium July 11-13, 2012.
• Zh. Zhusubaliyev, A. Churilov, and A. Medvedev, "Complex Dynamics and Chaos in a Scalar Linear Continuous System with Impulsive Feedback", 2012 American Control Conference, Montréal, Canada, June, 2012
• P. Mattsson and A. Medvedev, "Estimation of Input Impulses by Means of Continuous Finite Memory Observers", 2012 American Control Conference, Montréal, Canada, June, 2012
• Zh. Zhusubaliev, A. Churilov and A. Medvedev "Complex Dynamic Phenomena in a Low-Order Model of Non-Basal Testosterone Regulation", 50th IEEE Conference on Decision and Control, Orlando, FL, December, 2011.
• A. Churilov, A. Medvedev, and A. Shepeljavyi "Further Results on a State Observer for Continuous Oscillating Systems under Intrinsic Pulsatile Feedback", 50th IEEE Conference on Decision and Control , Orlando, FL, December, 2011.
• A. Churilov, A. Medvedev, A. Shepeljavyi. "State Observer for Continuous Oscillating Systems with Pulsatile Feedback", IFAC World Congress 2011, Milano, Italy, August-September.
• E. Hidayat and A. Medvedev. "Laguerre domain identification of continuous linear time delay systems from impulse response data", IFAC World Congress 2011, Milano, Italy, August-September.
• A. Churilov, A. Medvedev, A. Shepeljavyi,"Bifurcations in a mathematical model of non-basal testosterone production," 17th IFAC World Congress, Seoul, Korea, July 2008.
• A. Churilov, A. Medvedev, A. Shepeljavyi,"Periodic modes in a mathematical model of testosterone regulation," 3rd IFAC Workshop Periodic Control Systems (PSYCO'07), S:t Petersburg, 2007
• A. Churilov, A. Medvedev, A. Shepeljavyi,"Mathematical model of testosterone regulation by pulse-modulated feedback," IEEE Multi-conference on Systems and Control, Singapore, 2007.

Technical Reports

• E. Hidayat and A. Medvedev. "Parameter Estimation in a Pulsatile Hormone Secretion Model", Technical report, no. 2010-007, March, 2010, .pdf