-// /BBBBBB /ZZZZZZZZZZ \\-
--// | BB__/BB | ZZ_____ZZ \\--
---// | BB | BB | Z ZZ \\---
----// | BB | BB |/ ZZ \\----
-----// | BBBBBBB ZZ //-----
-----// | BB___/BB ZZ //-----
----\\ | BB | BB ZZ Z //----
---\\ | BB | BB ZZ ZZ //---
--\\ | BBBBBBBB ZZZZZZZZZZ //--
-\\ |/_______/ /_________/ //-
BZPhase: Program for Modeling and Building of 4D Phase Portraits of BZ reaction
For DOS 6 and higher with PMODE/W DOS Extender
For Windows95/NT with OpenGL
Version 1.0, 3 Feb 1997 VGA Graphic
Version 1.1, 14 Sep 1997
Version 1.2, 26 Mar 1998 VESA Graphic
Version 1.21, 28 Dec 1998
Version 1.3, 8 Feb 1999 OpenGL version
Created by
Post Graduate Student Andrew B. Ryzhkov
Under Graduate Student Arkady V. Antipin
under the supervision
Dr.Sci.(Chemistry) Alexander D. Karavaev
Dr.Sci.(Mathematics) Oleg V. Noskov
=====> Authors credits
For questions about the program,
E-Mail to Andrey B.Ryzhkov, RedAndr@usa.net and RedAndr@anrb.ru
or write to
Laboratory of Chemical Kinetics
Institute of Organic Chemistry
Ufa Research Centre
Russian Academy of Sciences
450054 Ufa, prospect Oktyabrya, 71
RUSSIA
WWW: http://members.tripod.com/~RedAndr/
Program's Manual
----------------
This file contains information about the working and usage of BZPhase.
NOTE:
This program is freeware. You may freely copy, distribute and change it.
Sources also available by request.
=====> Introduction.
The program BZPhase is intended for modeling of famous Belousov-Zhabotinsky
reaction and 4D phase portraits construction, in accordance with the model
based on the detailed eleven-stage scheme (Table 1 in Supl. 1) with some
modification: four variables had been included in rate constants.
The given reaction scheme show a variety of dynamics: from simple quasisinusoidal
oscillations to quasiperiodic, bursting, complex periodic and various chaotic ones
in following alternation order:
SS - QS - QP - B - CP - B - QP - QS - SS
where
SS = stationary state
QS = quasisinusoidal oscillations of low amplitude
QP = quasiperiodic regimes
B = bursting oscillations
CP = a complex succession of chaotic and periodic regimes
=====> System Requirements.
The following are minimum system requirements needed for work with the BZPhase:
CPU : 386DX-40
RAM : 8 Mb
Video : VESA 1.2 supporting card (e.g. S3 TrioV+)
Mouse : Microsoft compatible
Desirable configuration:
CPU : Pentium-133
RAM : 16 Mb
Video : VESA 2.0 supporting card with linear addressing (e.g. Matrox Millenium)
Mouse : Microsoft compatible
Optimal configuration:
CPU : PentiumMMX-266
RAM : 32 Mb
Video : VESA 2.0 supporting card with linear addressing (e.g. Matrox Millenium)
Mouse : Microsoft compatible
OpenGL version of the BZPhase needs Windows95-OSR2 or Windows NT.
For this version is desirable 3D Accelerator with OpenGL support.
=====> Running of the program.
Program may be run simply by typing : BZPhase.EXE .
File Param.Dat is parametric file.
It should contain initial conditions and parameters.
If it is not specified, the BZPhaze.Dat will be used by default.
To edit the parametric file, use EDIT.COM or another word processor.
Example:
BZPhase ShilAttr.dat
=====> View.
After calculations is done a phase portrait is being constructed.
On red axis is being ploted concentration of Br-.
On green axis is being ploted concentration of Me++.
On blue axis is being ploted concentration of Br2.
Color of points is fourth dimension. It is depended on concentration of Br'.
=====> Control.
Rotations of a phase portrait is controled by mouse and number-block of keyboard.
The following keys are being used:
'1'-'9','0' - how frequently points will be drawn
(1:1,1:2,1:5,1:10,1:20,1:50,1:100,1:200,1:500,1:1000)
'+','-' - to change, how frequently points will be drawn (with a step 100)
Tab - to connect points (on/off)
Blank - to display axes (on/off)
'S' - to save a phase portrait to the file BZPhase.plt (HP PLT format)
Esc - to exit from the program
=====> The contents of a parametric file.
Note that strings begining with semicolon is remarks.
; =============================================================
; Some information about current phase portrait
; =============================================================
; Regime approach time
5000
; Points count (maximum 150 000)
10000
; Integration step (points distance)
1
; Integration precision
1e-5
; =============================================================
; Constants of reaction rates (15)
2.10000000000E+0000
3.00000000000E+0006
4.20000000000E+0001
8.00000000000E+0004
3.00000000000E+0003
8.00000000000E+0009
4.60000000000E-0003
; Variable parameter
7e6
1.00000000000E+0006
2.00000000000E-0001
3.20000000000E+0009
1.00000000000E+0004
4.20000000000E+0007
8.90000000000E+0003
1.10000000000E+0002
; =============================================================
; Initial conditions: [Me+]o, [RH]o and [BrO3-]o (3)
5e-4
0.2
0.08
; =============================================================
; Begining Concentrations: [Br-]o, [HBRO2]o, [HOBr]o, [BrO2']o,
; [Me]o, [Br2]o, [R']o, [Br']o (8)
1e-5
0
0
0
0
0
0
0
0
; =============================================================
=====> Examples.
2_1000E6.DAT The limit cycle born after supercritical Hopf bifurcation at 2.091E6
2_1100E6.DAT The attracting to limit cycle
2_1180E6.DAT The T2-tore born after the second Hopf bifurcation at 2.117E6
2_1300E6.DAT The bursting oscillations
2_1400E6.DAT The bursting oscillations - the fractal tore
2_3000E6.DAT The chaos L3S8
2_4000E6.DAT The chaos L3S5
2_5200E6.DAT The toroidal chaotic attractor
2_5400E6.DAT The T2-tore
2_5700E6.DAT The limit cycle
3_0000E6.DAT -- // --
3_9300E6.DAT -- // --
5_2000E6.DAT -- // --
5_3000E6.DAT The doubling of limit cycle
5_3300E6.DAT The quadruplication of limit cycle
5_3400E6.DAT The chaos born after the Feigenbaum-like cascade of period doubling
6_0000E6.DAT The chaos L2S3
7_0000E6.DAT The spiral chaos
7_3318E6.DAT The gomoclinic chaos - Shil'nikov's attractor
7_4000E6.DAT The bursting oscillations transition to the tore and then to the limit cycle
7_4500E6.DAT -- // --
7_5000E6.DAT The limit cycle
7_6000E6.DAT The attracting to the limit cycle
7_7000E6.DAT The attracting to the stable stationary point
=====> Supplement 1. Scheme of the BZ-oscillator.
Reaction scheme Table 1.
(P.Ruoff and R.M.Noyes, J.Chem.Phys., 1986, V.84, 1413).
-------------------------------------------------------------------------
N | Reaction | Rate constant
----+---------------------------------------------------+----------------
1 | BrO3(-) + Br(-) + 2H(+) -> HBrO2 + HOBr | 2.1000000E+0000
2 | HBrO2 + HOBr -> BrO3(-) + Br(-) + 2H(+)| 1.0000000E+0004
3 | HBrO2 + Br(-) + H(+) -> 2HOBr | 3.0000000E+0006
4 | BrO3(-) + HBrO2 + H(+) -> 2BrO2' + H2O | 4.2000000E+0001
5 | 2BrO2' + H2O -> BrO3(-) + HBrO2 + H(+) | 4.2000000E+0007
6 | BrO2' + Me(+) + H(+) -> HBrO2 + Me(++) | 8.0000000E+0004
7 | HBrO2 + Me(++) -> BrO2' + Me(+) + H(+) | 8.9000000E+0003
8 | 2HBrO2 -> BrO3(-) + HOBr + H(+) | 3.0000000E+0003
9 | HOBr + Br(-) + H(+) -> Br2 + H2O | 8.0000000E+0009
10 | Br2 + H2O -> HOBr + Br(-) + H(+) | 1.1000000E+0002
11 | RH + Br2 -> RBr + Br(-) + H(+) | 4.6000000E-0003
12 | HOBr + R' -> ROH + Br' | 1E6..1E7
13 | RH + Br' -> Br(-) + H(+) + R' | 1.0000000E+0006
14 | RH + Me(++) -> Me(+) + H(+) + R' | 2.0000000E-0001
15 | 2R' + H2O -> RH + ROH | 3.2000000E+0009
-------------------------------------------------------------------------
where RH stands for malonic acid, and Me for metal ions.
The constant N12 is being used as a variable parameter which determines
the rate of Br- formation.
=====> Supplement 2. The ODE system of the BZ-oscillator.
BZ-oscillator is being described by the set of the eight ordinary
differential equations:
w1 =k[1] *cbro3*y[1] -k[2]*y[2]*y[3] ;
w2 =k[3] *y[1] *y[2] ;
w3 =k[4] *cbro3*y[2] -k[5]*y[4]*y[4] ;
w4 =k[6] *y[3] *(cme-y[4]) -k[7]*y[2]*y[5] ;
w5 =k[8] *y[2] *y[2] ;
w6 =k[9] *y[1] *y[3] -k[10]*y[6] ;
w7 =k[11] *crh *y[6] ;
w8 =k[12] *y[3] *y[7] ;
w9 =k[13] *crh *y[8] ;
w10=k[14] *crh *y[5] ;
w11=k[15]*y[7] *y[7] ; //___________________
//|_i_|_[Substance]_|
b[1]= -w1-w2-w6+w7+w9 ; //| 1 | [Br-] |
b[2]= w1-w2-w3+w4-2*w5 ; //| 2 | [HBrO2] |
b[3]= w1+2*w2+w5-w6-w8 ; //| 3 | [HOBr] |
b[4]= 2*w3-w4 ; //| 4 | [BrO2'] |
b[5]= w4-w10 ; //| 5 | [Me+] |
b[6]= w6-w7 ; //| 6 | [Br2] |
b[7]= -w8+w9+w10-2*w11 ; //| 7 | [R'] |
b[8]= w8-w9 ; //| 8 | [Br'] |
//-------------------
where
y[i] - concentration of i-th substance (see table above),
b[i] = d(y[i])/dt - rate of i-th substance changing,
k[i] - rate constant of i-th reaction,
cbro3 - stationary concentration of BrO3-,
crh - stationary concentration of RH,
cme - sum of Me+ and Me++ concentrations.
Modification of the closed system with permanent the initial concentrations
of BrO3- and RH is being used which allow one to obtain stationary regimes.
Also initial concentrations of H2O(1 M) and H(+)(1 M) is being maintained at
a steady level.
=====> Supplement 3.
The system of differential equations, in accordance with reactions (Table 1),
is being integrated by the (m,k)-method(*) with a given relative precision and
variable integration step (less than 1 s).
(*) Novikov V.A., Novikov E.A., Umatova L.A. Frezing of the Jacobi
matrix in the Rosenbrock type method of the second order
accuracy. //In proc. BAIL-IV Conf., Bool Press, 1986, p. 380-386.
Novikov E.A., Shitov Yu.A., Shokin Yu.I. One-step iteration-free
methods of solving stiff systems. // Soviet Math. Dokl., 1989,
v. 38, No. 1, p. 212-216.
=====> P.S.
If you will find errors in program or manual, don't hesitate to write us.
All remarks and wishes will be accepted with gratitude.