Pathogen populations may be stable, oscillating, or chaotic, depending on the value of lambda in the logistic difference equation. See Robert May’s comment on limits to growth: what stops cockroaches from taking over the universe?
The human body is a rainforest of microorganisms and anyone trying to diminish the population of pathogens or accelerate the growth of helpful organisms needs to understand the basics of evolutionary biology, the growth of populations, and environmental biology.
In particular, the basic mathematics of population growth must be understood to interpret the results of applying electoronic frequencies to populations of pathogens. A good summary of advances in thinking over the last century can be found on Arcytech’s site on Population Growth and Dynamics. In particular, the page on “Interesting Facts about Population Growth Mathematical Models” is worth reading.
You will find reference to Robert May’s 1976 paper in Nature (see abstract below) which introduced the concept of chaotic behavior into the mathematics of population growth. Professor May has an interesting summary of his findings in “The Chaotic Rhthyms of Life” where you will find a readable article on the logistic difference equation. A single parameter in this equation describes why electronic frequencies appear to work well sometimes and not well at all on other occasions.
In particular, this single parameter explains why electronic frequencies can help people feel better one day and worse the next. An endless cycle of good and bad days leads many people to conclude that electronic frequencies do not work, or are undependable. Much of this can be explained by the use of the wrong frequencies in trying to eliminate a microorganism. However, even with the right frequencies the power transfer from the electronic frequencies to the organism may be high or low and this directly affects the critical parameter in the logistic difference equation.
Let’s review Sutherland’s five rights for electronic medicine. The right power level applied to the right organ system with the right frequencies for the right amount of time using the right protocol will always kill a pathogen.
The power transfer can be such that the lambda parameter in the logistic difference equation is less than one. In that case you will be successful if you apply the frequency for a sufficient length of time. The time required is determined by how close lambda is to one. If power transfer can only bring lamda into the 1-3 range, you will have a stable population of pathogens that you cannot eliminate. If it is above three you will have chaotic behavior and large cycles of population growth and dieoff. This phenomenon is undoubtedly one of the contributors to lack of understanding of the so-called Herxheimer effect.
Power transfer can be significantly enhanced by exact frequencies, plate zapping, and the technology of the device applying frequencies. When you get poor results from electronic frequency devices it is important to get some expert help. Lack of power transfer sufficient to reduce lambda to less than one may explain many of your problems.
Simple mathematical models with very complicated dynamics
Nature. 1976 Jun 10;261(5560):459-67
First-order difference equations arise in many contexts in the biological, economic and social sciences. Such equations, even though simple and deterministic, can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hiearchy of stable cycles, to apparently random fluctuations. There are consequently many fascinating problems, some concerned with delicate mathematical aspects of the fine structure of the trajectories, and some concerned with the practical implications and applications. This is an interpretive review of them.