Chaos suppression

Guidi, G.M., J. Halloy A. Goldbeter. 1995. Chaos suppression by periodic forcing Insights from Dictyostelium cells, from a multiply regulated biochemical system, and from the Lorenz model. In Chaos and Complexity. J. Trfin Thanh Vin et al, eds. Editions Frontieres, Gif-sur-Yvette, France, pp. 135-46. 

C. Keel, U. Schnider, M. Maurhofer, C. Voisard, J. Laville, P. Burger, D. Ha,ss, and G. Defago, Suppression of root diseases by Pseudomonas fluorescens CHAO importance of the bacterial secondary metabolite 2,4-diaceiylphloroglucinol, Molecular Plant-Microbe Interactions 5 4 (1992). 

In such cases, we could try to reduce the high-frequency output noise by suppressing it at the input. So that could be a valid reason to place a small ceramic capacitor at the input of an older-generation switcher IC (i.e., one with a BJT switch). Its primary purpose is then not to ensure that the control does not go into chaos because of switch transient noise, but to reduce the output noise in noise-sensitive applications. 

Pushkareva, M., Chao, R., Bielawska, A., Merrill Jr, A.H., Crane, H.M., Lagu, B., liotta, D. and Hannun, Y.A., 1995, Stereoselectivity of induction of the retinoblastoma gene product (pRb) dephosphorylation by D-erythro-sphingosine supports a role for pRb in growth suppression by sphingosine, Biochem. 34 1885-1892. 

Substances destroying the water structure, fhe so-called chao-tropic substances such as urea, guanidinium hydrochlorid, or some organic solvents such as mefhanol, efhanol, or acetonitrile, suppress hydrophobic interactions. Ions also alter the water structure. The power of destruction of water structure is given by the Hofmeister series ... 

Wolf WC, Evans DM, Chao L, Chao J. A synthetic tissue kallikrein inhibitor suppresses cancer cell invasiveness. Am J Pathol 2001 159 1797-1805. 

With chaos in classical dynamical systems well established, the question arises whether quantum systems axe able to display exponential sensitivity and chaos. The answer is that most quantum systems do not. Not even if their classical counterparts axe chaotic. We can say that chaos is suppressed on the quantum level. An example of this suppression... 

Bliimel, R. and Smilansky, U. (1990a). Quantum mechanical suppression of chaos. Physics World 3(2), 30-34. 

As a consequence of the collective motion of the neutral system across the homogeneous magnetic field, a motional Stark term with a constant electric field arises. This Stark term inherently couples the center of mass and internal degrees of freedom and hence any change of the internal dynamics leaves its fingerprints on the dynamics of the center of mass. In particular the transition from regularity to chaos in the classical dynamics of the internal motion is accompanied in the center of mass motion by a transition from bounded oscillations to an unbounded diffusional motion. Since these observations are based on classical dynamics, it is a priori not clear whether the observed classical diffusion will survive quantization. From both the theoretical as well as experimental point of view a challenging question is therefore whether quantum interference effects will lead to a suppression of the diffusional motion, i.e. to quantum localization, or not. 

It is obvious that the manipulated brain of the masses, filled from birth with emotional misbeliefs, illusions, misinterpretations, myths, fantasies, motivates - given the right circumstances - irrational activities. In peaceful periods of the community rational brain activity is dominant and the irrational, emotional chaos is suppressed. There are specially organized occasions for the eruption of the volcano (concerts, sport-events, proper political party meetings, etc.). But in emotionally supersensitive, trying periods of the community (riots, revolutions, wars) the irrational brain becomes dominant. The immense literature that describes the history of mankind is, as a matter of fact, an exact description of the consequences of traditional manipulation of the human brain. 

Yet another possibility is that part of the cells within a continuously stirred suspension would oscillate in a chaotic manner if left on their own, while the remaining cells would oscillate periodically in the absence of the chaotic population. The coupling of the two populations within the same suspension could well suppress any manifestation of chaos by conferring upon the coupled system a global, regular behaviour. 

Suppression of chaos by periodic oscillations An intriguing property illustrated by the bifurcation diagram of fig. 6.20 is that the behaviour of the mixed suspension is strongly tilted towards periodic behaviour. To examine this phenomenon in more detail, it is useful to focus on the simple case where the two populations differ only... 

Fig. 6.23. Minimum fraction of periodic cells suppressing chaos, (a) The value of the minimum fraction of cells from periodic population 2 in the final suspension, Fjniin, capable of transforming chaos of population 1 into simple periodic oscillations is plotted as a function of parameter k 2> the chaotic behaviour of population 1 is that shown in fig. 6.21 (upper panel, left). The curve was generated according to eqn (6.11) with /ceJ = 2.6257 min" and = 2.6167 min", (b) Plotted as a function of V2 is the value of the minimum fraction of periodic cells from population 2 needed to transform the chaotic behaviour of population 1 into (i) simple periodic oscillations, and (ii) oscillations of period 8, with eight peaks of cAMP per period. The results are obtained numerically by integration of eqns (6.9) (dots) as described in the legend to fig. 6.21. The values = 2.625 min" and Vi/jU. = 1.4073825 min" are taken for the chaotic population other parameter values are as in fig. 6.2. The vertical, dashed line indicates the value of kei or Vj giving rise to chaos in population 1 (Li et al, 1992a).

The above discussion focused on the suppression of chaos by periodic oscillations. As shown by the bifurcation diagram in fig. 6.3, other dynamic transitions may be brought about by the coupling of two populations endowed with distinct d5mamic properties the global behaviour... 

Suppression of chaos by the periodic fordng of a strange attractor... 

Fig. 6.24. Suppression of chaos by a small-amplitude, periodic input of cAMP. The chaotic oscillations of cAMP (b) are the same as those considered in fig. 6.21 (top, left part). The system is subjected to a sinusoidal input of cAMP (a), as described by eqn (6.3d). Such forcing of the strange attractor leads to periodic oscillations of cAMP (c) the latter are obtained by numerical integration of the first two equations of system (6.3) and eqn (6.12) for A = 0.025 and r = 6 min (Li et ai, 1992b).

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