Topic
Bifurcation diagram
About: Bifurcation diagram is a research topic. Over the lifetime, 8379 publications have been published within this topic receiving 139664 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: Chow and Hale as discussed by the authors used a third order Picard-Fuchs equation to show that a certain two parameter family of vector fields for parameter values in a certain cone has a unique limit cycle, which is born from a Hopf bifurcation and dies in a saddle connection.
39 citations
TL;DR: It is shown that a three-neuron cascaded network can serve as a universal oscillator, whose amplitude and frequency can be completely controlled by input parameters.
39 citations
TL;DR: In this article, a bifurcation theory for a system of globally coupled phase oscillators is developed based on the theory of rigged Hilbert spaces, and it is shown that there exists a finite-dimensional center manifold on a space of generalized functions.
Abstract: A bifurcation theory for a system of globally coupled phase oscillators is developed based on the theory of rigged Hilbert spaces. It is shown that there exists a finite-dimensional center manifold on a space of generalized functions. The dynamics on the manifold is derived for any coupling functions. When the coupling function is $\sin \theta $, a bifurcation diagram conjectured by Kuramoto is rigorously obtained. When it is not $\sin \theta $, a new type of bifurcation phenomenon is found due to the discontinuity of the projection operator to the center subspace.
39 citations
TL;DR: In this paper, a discrete-time chaos generator implemented with two nonlinear circuit cells has been fabricated in a 0.6?m CMOS technology, where each cell is creating a function (map) which allows a chaos signal to be generated.
Abstract: A discrete-time chaos generator implemented with two nonlinear circuit cells has been fabricated in a 0.6 ?m CMOS technology. Each cell is creating a function (map) which allows a chaos signal to be generated. Measurements of the chip were performed with a supply voltage of 5 V, up to a frequency of 2.5 MHz. A bifurcation diagram of the circuit and the Lyapunov exponent calculation are presented. The size of the generator layout (without the switches) is 32 × 19 ? m which makes it suitable for applications where many chaos signal generators are required on a single chip.
39 citations
TL;DR: A novel first-order delay differential equation capable of generating n-scroll chaotic attractor is presented and the results show that the system has a chaotic regime in a wider parameter range.
Abstract: In this paper, a novel first-order delay differential equation capable of generating n-scroll chaotic attractor is presented Hopf bifurcation of the introduced n-scroll chaotic system is analytically and numerically determined The bifurcation diagram and Lyapunov spectrum of the system are calculated and the results show that the system has a chaotic regime in a wider parameter range Furthermore, period-3 behavior has been observed on the system Circuit realizations of two-, three-, four-, and five-scroll chaotic attractors are also presented
39 citations