Chaos in the Belousov-Zhabotinsky Reaction
نویسندگان
چکیده
In this project, we investigate two different models of the Belousov-Zhabotinsky Reaction, the Oregonator (1973) and a model found in a 1992 paper by Györgyi and Field. We discuss the original literature and then numerically investigate both models. We find the the Oregonator is not chaotic, and that the Györgyi-Field model is for certain values of a variable parameter. For each model, we solve its system of ordinary first order differential equations, plot the 3-dimensional attractor, find its correlation dimension, calculate the Lyapunov exponents, and construct time-delay plots. For the Györgyi-Field model, we also produce a bifurcation plot, which shows what values of a certain parameter cause chaos in the system.
منابع مشابه
Experimental demonstration of subtleties in subharmonic intermittency
Experiments on the Belousov-Zhabotinsky reaction in a well-stirred flow reactor elucidate one of the routes to chaos, subharmonic intermittency (type III interminency). Measurements conducted as a function of two independent control parameters demonstrate how difficult it is in practice to distinguish this route to chaos from subcritical period doubling transitions with similar chaotic time sig...
متن کاملComplexity in Chemical Systems
The mechanistic origins of complex responses in chemical systems are traced to the role of chemical or thermal feedback arising from autocatalysis or self-heating. These simple building blocks, which occur widely in chemistry and biochemistry, support behavior ranging from simple clock reactions to sustained oscillations, chaos and spatial pattern formation. Examples discussed include the Belou...
متن کاملOn the Origin of Chaos in the Belousov-Zhabotinsky Reaction in Closed and Unstirred Reactors
We investigate the origin of deterministic chaos in the Belousov–Zhabotinsky (BZ) reaction carried out in closed and unstirred reactors (CURs). In detail, we develop a model on the idea that hydrodynamic instabilities play a driving role in the transition to chaotic dynamics. A set of partial differential equations were derived by coupling the two variable Oregonator–diffusion system to the Nav...
متن کاملEncoding information in chemical chaos by controlling symbolic dynamics
In this paper we describe a technique of encoding and then decoding symbol sequences containing information into chaotic oscillations of the Belousov-Zhabotinsky reaction. The encoding technique is based on controlling the chaotic oscillations by applying small parameter perturbations and on learning the grammar of corresponding symbol dynamics produced by the free-running chaotic system. The u...
متن کاملIdentification of Excitable Media Using a Scalar Coupled Map Lattice Model
The identification problem for excitable media is investigated in this paper. A new scalar coupled map lattice (SCML) model is introduced and the orthogonal least squares algorithm is employed to determinate the structure of the SCML model and to estimate the associated parameters. A simulated pattern and a pattern observed directly from a real Belousov–Zhabotinsky reaction are identified. The ...
متن کامل