R S Peters; Postscript 2, Journal of Philosophy of Education, Volume 7, Issue 2, 30 May 2006, Pages 179–180, https://doi.org/10.1111/j.1467-9752.1973.tb00480.x.

In this paper, the Helmholtz equation with quadratic damping themes is used for modeling the dynamics of a simple prey-predator system also called a simple Lotka–Volterra system. From the Helmholtz equation with quadratic damping themes obtained after modeling, the equilibrium points have been found, and their stability has been analyzed. Subsequently, the harmonic oscillations have been studied by the harmonic balance method, and the phenomena of resonance and hysteresis are observed. The primary and secondary resonances have been researched by the (...) multiple-scale method, and the conditions of stability of the amplitudes of oscillations are determined. Chaos is detected analytically by the Melnikov method and numerically using the basin of attraction, the bifurcation diagram, the Lyapunov exponent, the phase portrait, and the Poincaré section. The effects of all the parameters of the system are analyzed in detail, and special emphasis is placed on the new parameters. Through this analysis, the complex phenomena such as hysteresis, bistability, amplitude jump, resonances, and chaos have been obtained. The control of the parameters and the necessary conditions to control the aforementioned phenomena have been found. (shrink)

R T Allen; The Philosophy of Michael Polanyi and its Significance for Education, Journal of Philosophy of Education, Volume 12, Issue 1, 30 May 2006, Pages 167–.

The mutakallimūn, who began to take care of nature as a result of their metaphysical concerns from the early period and with the influence of the dualist and materialist groups, suggested various theories that attempt to explain the structure and functioning of the universe. Over time, many subjects of physics became an indispensable part of Kalām and were used in the proof of the fundamental principles. Thus, in addition to the definition of body (jism), Kalām books began to contain detailed (...) topics such as time, space, movement and distance. After summarizing the definitions of body, which were made by the mutakallimūn, this article will examine the contents of Ibn Kamāl's epistle on ṭafra (leaping), which has many copies with various titles in the Turkish Libraries. In the beginning of the epistle, Ibn Kamāl mentions the descriptions of body suggested by the prominent mutakallimūn, and then, he compares the views of al-Naẓẓām, who believes in the finite division, with atomist mutakallimūn who accept the infinite division. He criticizes the idea of ṭafra with regard to the notion of body in Kalām. After explaining the arguments of both groups with their justifications, he points out the weaknesses of the arguments of each group, as well. In this connection, he revisits the theory of ṭafra, which is, he argues, a mandatory consequence of al-Naẓẓām’s definition of object, as he also reviews the opinions of Quṭb al-Din al-Rāzī in this direction. (shrink)