2.3 Model " Family History "

Consider a family consisting of husband, wife and his mother. It is assumed that in-law and daughter are in the warm family relationships, struggling to assert its influence on the only man in the family. And he , poor man , torn between passionate love to his mother and wife. State functions here will influence and power, respectively, and mother-in -law on his beloved son and husband.

It is assumed that the influence of the rate of change of each value is proportional to the women of this magnitude . As in-law and daughter have a great relationship with the " head of the family " , so that the growth of their influence certainly includes some positive value , defined by the value of the woman in the eyes of men . If the impact of growth limited only by this factor, we would observe the unlimited growth of influence of each of the women. In practice, the growing influence of naturally constrained . In particular, there is also the impact of the fall , which is characterized by the expression - where the parameter characterizes the decreasing influence of the i-th woman defined by her personal shortcomings in the eyes of men . Finally, in-law and daughter-in striving to reduce the impact of man on the opponent , so that increase the impact of i-th woman also includes negative expression - where the constant characterizes the degree of antipathy towards this woman of her rival .

On the basis of the assumptions made, we conclude that the study process is described by the following system of equations:

Initial conditions: ,

The resulting ratios correspond to the model considered in the theory of niche with all the ensuing consequences. Depending on the combination of parameters events may develop in the following different scenarios.

When inequalities

, ,

Wife - in all respects -in-law loses . As a consequence, its impact on the spouse is gradually eroding, which inevitably entails a divorce or at least implicitly submission strong and domineering sister -in-law . Opposite contrast ratio means a complete defeat in-law. It either submits more energetic sister- or settled separately from ungrateful spouses. In this scenario, the schedule will be as follows:

Condition

, ,

indicate equality of forces opposing sides. Cute personages continue to lead active hostilities with varying success, and none of them is able to finally prevail.

Inequalities

, ,

Correspond to the case did not play a decisive role personal qualities of women (the merits of shortcomings), and the degree of their mutual antipathy. Outcome here leaves much to be desired - depending on the initial state of the system (the relationship with a man warring parties to the top of their cohabitation) wins the full or daughter-in-law either. Finally, there is another option, characterized by conditions

inequalities

,

Where for which the personal qualities of women take precedence over their mutual antipathy. Each of them finds a niche in the family and eventually peace and tranquility reigns.

Now, it is possible to add two additional factors: