Cobweb diagram

The corresponding cobweb diagram is impressively complex (Figure 10.2.6). 

A cobweb diagram reveals how flip bifurcations can give rise to perioddoubling. Consider any map f, and look at the local picture near a fixed point where / x ) —1 (Figure 10.3.3). 

Prove that x = 0 is a globally stable fixed point for the map = -sinx . (Hint Draw the line = —x on your cobweb diagram, in addi-... 

A superstable cycle) Consider the logistic map with r= 3.7389149. Plot the cobweb diagram, starting from x = y (the maximum of the map). You should find a superstable cycle. What is its period ... 

In the cobweb cycle, as drawn in Fig. X.2, the equilibrium is unstable. Any small perturbation will set up an ever-widening cycle. By the same token, if the farmers begin out of equilibrium, they will never come near it. If we draw the diagram differently, with the supply curve steeper than the demand curve, the opposite is true. After a while, the farmers converge to the equilibrium and return to it after any accidental perturbation. A preliminary conclusion might be that the realization of an equilibrium depends on details of the interaction. Some deviations from equilibrium correct themselves, while others get out of hand. 

Solvent choice also affects application properties. True solvents, such as toluene or 1,1,1-trichloroethane, give stronger solutions which tend to be more stringy and cobweb when sprayed. Improved application properties are obtained by using a blend which falls closer to the shady area of the kidney shaped solvent diagram. For example, spray able adhesives are generally based on fast-evaporating solvent blends which fall in the upper left quadrant of Fig. 6. 

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