1. The child is born in the family.
2. Sudden illness Moms.
1. Suppose that before the advent of the first factor, the family also occurred with "invisible war" in which there was no winner yet. For such conditions would be fair to the following inequality:
Е1/а11 > Е2/а21 Е1/а12 < Е2/а22 1/2 > 2/5, 1/3 > 2/4
But, at some point in time after the birth of the baby, E2 (the degree of influence of his wife) dramatically increase several times. Then their struggle will be as follows:
2. In case of sudden illness in-law, then E1 (degree of influence of the mother) increases. Then
Е1/а11 > Е2/а21 Е1/а12 < Е2/а22 1/2 > 2/5, 1/3 > 2/4
The described model does not take into account the response to the events of the culprit and the subject of conversation. However, is it really necessary to ask the opinion of authoritative head of the family, when a serious dispute is between loving representatives of the weaker sex? However, the relationship between mother-in-law characterized by exciting events.
2.4 Investigation of the stability of the mathematical model
Explore our mathematical model on Lyapunov stability.
Determination of Lyapunov's theorem on stability:
Consider the system of differential equations
(1)
Decision
problem (1), (3) is called Lyapunov stable if
such that for any solution
this equation that satisfies
First we need the right side of the equation set equal to zero. It turns out the root of the equation will be:
Using code written in C + +, we obtain the following graphs:
Using the graph , we see that the introduction of any positive values for all variables , functions will tend either to zero or to its second root of the equation , which confirms the stability function.
2.5 Model Trade union activities
Consider a simple dynamic model of trade union activities in the workplace. State functions here are the degree of influence of the trade union and social conditions in the considered company. It is assumed that the significant deterioration of social conditions influence the union grows with some speed, and in the absence of trade union influence social conditions deteriorate at a constant rate . The growing influence of the trade union is accompanied by improvement of social conditions, which in turn leads to a drop in trade union influence . Thus, the mathematical model of the process takes the form:
The initial conditions for this type of equations is:
Where the constants r1 and r2 are the parameters of the problem.
Assign the value of e1 = 0.5, e2 = 2. then schedule for our equation is as follows:
These equations can be found in the description of chemical, biological and economic processes. As you know, they have a periodic solution ( Fig.45) . If at the initial time of the trade union influence is quite weak, and social conditions - low , then the right side of the first equation is positive, and the second - negative. Thus, at the first stage of an increase in the influence of the union ( more workers in poor social conditions in the production of turns for help to the union ) and the further deterioration of social conditions (with a weak union influence greedy businessman tries to maximize profits at the expense of the brutal exploitation of disenfranchised workers ) . With the growing influence of the union certainly comes a point of transition to the second stage, when the entrepreneur is forced to reckon with the union and threatened strike goes to the just demands of a certain satisfaction of their employees. Occurs at improving social conditions continue to increase the influence of the trade union , which enjoys increasing support for workers and employees. However, with the rise in living standards ungrateful people gradually eliminates the need to support the union.
In the third stage the influence of the trade union starts to fall, while the social conditions in the production still growing because the union is still strong enough, but because the entrepreneur does not perform any risk of bad events. However, with the fall of union influence greedy owner starts to fight for increasing their income.
In the fourth stage there is a further decline in trade union influence (social conditions are still relatively high, and the union has not had time to gain momentum) and the deterioration of living conditions. As the deterioration of the standard of living over time, the union again restores its influence and the process repeats.
Fig.45. Oscillation influence of trade union and social conditions in the production