Related papers: Self-Excited Oscilations : from Poincar\'e to Andr…
The concept of "limit cycle" was introduced by Henri Poincar\'e in his second memoir "On curves defined by a differential equation" in 1882. From the point of view of physics, a stable limit cycle (or attractive) is the representation of…
At the beginning of the twentieth century while Henri Poincar\'e (1854-1912) was already deeply involved in the developments of wireless telegraphy, he was invited, in 1908, to give a series of lectures at the \'Ecole Sup\'erieure des…
From 28 to 30 January 1933 was held at the Institut Henri Poincar\'{e} (Paris) the first International Conference of Nonlinear Oscillations organized at the initiative of the Dutch physicist Balthazar Van der Pol and of the Russian…
Relaxation oscillations are commonly associated with the name of Balthazar van der Pol via his eponymous paper (Philosophical Magazine, 1926) in which he apparently introduced this terminology to describe the nonlinear oscillations produced…
In 1893, the "physicist-engineer" Andr\'e Blondel invents the oscilloscope for displaying voltage and current variables. With this powerful means of investigation, he first studies the phenomena of the arc then used for the coastal and…
A limit cycle is a self-sustained periodic motion appearing in autonomous ordinary differential equations. As the period of the limit cycle is a-priori unknown, it is challenging to find them as stationary states of a rotating ansatz.…
A periodically forced oscillator in a model for seasonality shows stability pockets and chains thereof in the parameter plane. The frequency of the oscillator and the season indicated by a value between zero and one are the two parameters.…
In this article is shown that large systems endowing phase coexistence display self-oscillations in presence of linear feedback between the control and order parameters, where an Andronov-Hopf bifurcation takes over the phase transition.…
Before 1905, Poincar\'e stressed the importance of the method of clocks and their synchronization, but unlike Einstein, magnet and conductor (asymmetries in Lorentz's theory regarding the explanation of Faraday's induction) or chasing a…
This paper reviews a paper from 1906 by J. Henri Poincar\'e on statistical mechanics with a background in his earlier work and notable connections to J. Willard Gibbs. Poincar\'e's paper presents important ideas that are still relevant for…
Errors are found in example problems from Henri Poincar\'e's paper ``M\'emoire sur les courbes d\'efinies par une \'equation diff\'erentielle.'' Examples four and five from chapter seven and examples one, two, and three from chapter nine do…
A system of autonomous differential equations with a stable limit cycle and perturbed by small white noise is analyzed in this work. In the vicinity of the limit cycle of the unperturbed deterministic system, we define, construct, and…
This study investigates the existence and stability of limit cycles resulting from self-excited oscillations in linear multi-degree-of-freedom systems subjected to discontinuous, state-dependent forcing. Using the method of averaging and…
Based on Feynman's lifetime efforts on quantum mechanics and relativity, it is concluded that the basic difference between field theory and string theory is that field theory is based on running waves while string theory should deal with…
Henri Poincare Saint Louis lecture, delivered on 24 September 1904 at the International Congress of Arts and Science, occupies a distinctive place in the pre history of twentieth century theoretical physics. In this text, Poincare…
In the context of studying periodic processes, this paper investigates first under which conditions switching affine systems in the plane generate stable limit cycles. Based on these conditions, a design methodology is proposed by which the…
In 1967 Winfree proposed a mean-field model for the spontaneous synchronization of chorusing crickets, flashing fireflies, circadian pacemaker cells, or other large populations of biological oscillators. Here we give the first bifurcation…
In this work, our primary goal is to study the Poincare map and the existence of limit cycles for Welander's model that describes ocean convection. Welander developed two versions of his model, one with a smooth transition between…
Steady states of alternating-current (AC) circuits have been studied in considerable detail. In 1982, Baillieul and Byrnes derived an upper bound on the number of steady states in a loss-less AC circuit [IEEE TCAS, 29(11): 724--737] and…
Within the framework of relativistic cosmology oscillating or cyclic models of the universe were introduced by A. Friedmann in his seminal paper of 1922. With the recognition of evolutionary cosmology in the 1930s this class of closed…