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Positive and Negative Feedback in Engineering and Biology

E. S. Zeron (2008)

Mathematical Modelling of Natural Phenomena

No other concepts have shaken so deeply the bases of engineering like those of positive and negative feedback. They have played a most prominent role in engineering since the beginning of the previous century. The birth certificate of positive feedback can be traced back to a pair of patents by Edwin H. Armstrong in 1914 and 1922, whereas that of negative feedback is already lost in time. We present in this paper a short review on the feedback's origins in the fields of engineering and biology....

Positive fixed point theorems arising from seeking steady states of neural networks

Gen Qiang Wang, Sui-Sun Cheng (2010)

Mathematica Bohemica

Biological systems are able to switch their neural systems into inhibitory states and it is therefore important to build mathematical models that can explain such phenomena. If we interpret such inhibitory modes as `positive' or `negative' steady states of neural networks, then we will need to find the corresponding fixed points. This paper shows positive fixed point theorems for a particular class of cellular neural networks whose neuron units are placed at the vertices of a regular polygon. The...

Positive periodic solution for ratio-dependent n -species discrete time system

Mei-Lan Tang, Xin-Ge Liu (2011)

Applications of Mathematics

In this paper, sharp a priori estimate of the periodic solutions is obtained for the discrete analogue of the continuous time ratio-dependent predator-prey system, which is governed by nonautonomous difference equations, modelling the dynamics of the n - 1 competing preys and one predator having nonoverlapping generations. Based on more precise a priori estimate and the continuation theorem of the coincidence degree, an easily verifiable sufficient criterion of the existence of positive periodic solutions...

Positive solutions of a renewal equation

Janusz Traple (1992)

Annales Polonici Mathematici

An existence theorem is proved for the scalar convolution type integral equation x ( t ) = ∫ - ∞ ∞ h ( t - s ) f ( s , x ( s ) ) d s .

Possibly Longest Food Chain: Analysis of a Mathematical Model

T. Matsuoka, H. Seno (2008)

Mathematical Modelling of Natural Phenomena

We consider the number of trophic levels in a food chain given by the equilibrium state for a simple mathematical model with ordinary differential equations which govern the temporal variation of the energy reserve in each trophic level. When a new trophic level invades over the top of the chain, the chain could lengthen by one trophic level. We can derive the condition that such lengthening could occur, and prove that the possibly longest chain is globally stable. In some specific cases,...

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