Indices IV.

Correlation between qualitative changes and time and space In the first piece of the series the correlation between qualitative chamges and stability reserve was defined. Let us now have a look at the relationship between these on the one hand, and between qualitative changes and time and space on the other. It will be demonstrated…

The Law of Bodies Coiling onto Each Other

I have no knowledge of this law of physics having been published before, but as this is not my field of research, I may be wrong. The law: All bodies capable of coiling onto each other will spontaneously coil onto each other. This is a genuine law, even though it sounds like one of Murphy’s…

Indices III.

How general are the notions relating to the indices of stability? They are among the most general notions of science. The reason for this is that a system can only exist if its indices of stability bear a positive sign. This alters Hegel’s well-known axiom to the following: ONLY QUANTITATIVE CHANGES REVERSING A SYSTEM’S INDICIES…

Equality of Coordinate Systems

According to the literature of mathematics, right angular and polar coordinate systems are of equal value. This means that it is possible to transfer from one to the other without loss of data. The transfer is done with the application of a few simple formulas. In the case of a plane, – when transferring from…

Two-Dimensional Lottka-Volterra

Here dx1/dt = r1x1 + a11x12 + a12x1x2 = P (1a) dx2/dt = r2x2 + a21x1x2+ a22x22 = Q (1b) with r being the intrinsic growth rate of the living thing (group of living things) within those examined, and a being an interaction term. The singular point is P = Q = 0 P is…

Generalization of Phase-Plain Methods

In case the singular formation is a point, the following hold true: 1 Let w be a vector corresponding with a process variable shown as a local coordinate; u, the time change vector of this; w0 and u0, their value in the singular point. Also, let r = w – w0 v = u (as…

Theorem of Asymptotic Stability

1 A sufficient precondition of asymptotic stability 1.1. Basis 1.1.1 Circle, spherical surface A circle, a spherical surface, and its n-dimensional equivalent are the geometrical place of those points which in the plain, in space and in the n-dimensional space are at an equal distance from a given point, the so-called center. Because of this,…

Indices II.

Stability Reserve as a Panacea To make mathematics more popular, it is important to show how the average person comes into contact with a term, thesis etc. in everyday life. That is what this piece is for. Why is it that a cure is effective in the case of some people while it is not…

One-dimensional Lottka – Volterra

“These encounters have a positive or negative effect on population i described by the sign and magnitude of their interaction term aij, and an effect on population j described by the corresponding term aji. If aij is negative, encounters with j are detrimental to i, while if it is positive, these encounters are beneficial to…

Indices

Indices of the Stability of Dynamic Systems In the previous pieces of this series of articles I added new concepts to already existing groups of concepts. In this writing and in the ones to follow, however, I will introduce a hitherto non-existent group of concepts and will expound on the components of this group of…