Journal of Applied Nonlinear Dynamics 2(3) (2013) 285–301 Journal of Applied Nonlinear Dynamics https://lhscientificpublishing.com/Journals/JAND-Default.aspx Numerical Study on Bray-Liebhafsky Oscillatory Reaction: Bifurcations Branislav Stankovi´ c 1† , ˇ Zeljko ˘ Cupi´ c 2 , Nataˇ sa Peji´ c 3 and Ljiljana Kolar-Ani´ c 1 1 Faculty of Physical Chemistry, University of Belgrade, Studentski trg 12-16, 11000 Belgrade, Serbia 2 Institute of Chemistry, Technology and Metallurgy, University of Belgrade, Department of Catalysis and Chemical Engineering, Njegoˇ seva 12, 11000 Belgrade, Serbia 3 Faculty of Pharmacy, University of Belgrade, Vojvode Stepe 450, 11000 Belgrade, Serbia Submission Info Communicated by Albert C.J. Luo Received 1 February 2013 Accepted 25 March 2013 Available online 1 October 2013 Keywords Bray-Liehafsky oscillatory reaction Chemical reaction Andronov-Hopf bifurcation Saddle-loop bifurcation Abstract The time series obtained by numerical simulations of the model of the Bray-Liebhafsky oscillatory reaction is analyzed under the continuously fed well stirred tank reactor (CSTR) conditions, with the aim to find bifurcation points in which system of Bray- Liebhafsky oscillatory reaction transforms from stable to unsta- ble state and vice versa. Types of bifurcation points, supercrit- ical and subcritical Andronov-Hopf bifurcation and saddle-loop bifurcation are determined from characteristic scaling laws. © 2013 L&H Scientific Publishing, LLC. All rights reserved. 1 Introduction Different dynamic states such as periodic and aperiodic oscillatory ones including mixed-mode and chaotic evolutions, together with characteristic transitions between them in bifurcation points, can be found in almost all complex nonlinear reaction systems with feedback. Although such systems in their phase space defined by corresponding control parameters should be mostly in stable steady states, there are lots of them (particularly in biochemical and social sciences) which are always in various oscillatory dynamic states. Such examples are the double oscillatory evolution of endocrine hormones at humans with different periods on the ultradian and circadian levels [1– 7], oscillations of glycolytic intermediates [8–10], heart beating, etc. There are also, dynamical systems that are not always in such states, but can be often found in them: chemical systems, such † Corresponding author Email address: branislav20@yahoo.com ISSN 2164 - 6457, eISSN 2164 - 6473/$- see front materials © 2013 L&H Scientific Publishing, LLC. All rights reserved. DOI : 10.5890/JAND.2013.08.004