By Okan Gurel

Content material: varieties of oscillations in chemical reactions / O. Gurel, D. Gurel -- fresh advancements in chemical oscillations / D. Gurel, O. Gurel

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Extra resources for Oscillations in Chemical Reactions

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IV. 1. X Boundedness t Fig. 1. Oscillatory solution in one-dimensional representation Here t is the time element of the dynamic (kinetic) system, x is the variable, concentration of a chemical element of the reaction. This representation is suitable if one is interested particularly in both amplitude (measured along the x-axis), and period (measured along the t-axis), both being (quantitative characteristics). g. x and y by plotting multiple graphs for (x, t), (y, t), .... The only qualitative information we get is that x is bounded.

Classification of Abstract Models by Right-Hand Sides ] Model stant x i 1975-1 1976-1 Y z x2 y~ ? A B C kl t --k2 kl* I kl [ k6 k2 k5 i k7 D1 --k3 --k2 k4 --k5 ! l ! I I --k3 1 --k4 --k3 --k6 k8 --k9 --kl0 I_ where A = xy/(k + x), B = xy/(k + y), C = xz/(k + x), D1 = z/(k* + z). Model 1 Constant x 1976-2 y --I 1 l 976-4 z xz yz x~ y2 za & --1 a --C b d xy 1 --1 1 --1 --a b --c 53 O k a n Gurel a n d D e m e t Gurel Table I l L (continued) Model Con~ant 1977-4 xy y Z --1 --1 a --b xz ? [A1 --a --a 1979-I / yz --1 1 1 C 1979-3 --1 1 --1 --a be 1979-4 --a --1 d where Model 1 --b b --1 c --I --1 a --b --1 f 1979-5 1981 a3 a2 a3 --a 1977-3 --1 --1 al --a5 --kl* 1 a4 --1 i --k5* i :o=t Z A B --1 kl k2' k5 k7 kl --k4 --k3 --k6 --k3 k2' k4 --k5 ml m4 --1 m2 m5 F1 --F1 1+7 1977-5 where --a D = y z / ( k , + y) , F2 --m3 --m6 E1 = e(x 2 + f ) z/(z + k3) , FI = zy2 E2 = - - k 8 z/(z + k ) , rl=yx ~ .

2. One singular solution. 3. Two singular solutions, one saddle ($2) , one unstable focus (S1) and a stable limit cycle. 4. S I stable, S2 saddle, and S 1 surrounded by an unstable limit cycle. 5. S l stable, S2 saddle, S 1 surrounded by unsable limit cycle which is surrounded by a stable limit cycle. 6. S 1 unstable, S 2 saddle. ,_utc \ \ J Fig. 22. Coexistence of stable limit cycle and stable singular point surrounded by an unstable limit cycle, (After Dynnik et al. (1973)) I Model 6: Reference: Dynnik and Set'kov ( t 975-1).

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