Phase Diagram for the Winfree Model of Coupled Nonlinear Oscillators

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 analysis of the model, for a tractable special case. The system displays rich collective dynamics as a function of the coupling strength and the spread of natural frequencies. Besides incoherence, frequency locking, and oscillator death, there exist novel hybrid solutions that combine two or more of these states. We present the phase diagram and derive several of the stability boundaries analytically.Comment: 4 pages, 4 figure

Stochastic averaging using elliptic functions to study nonlinear stochastic systems

In this paper, a new scheme of stochastic averaging using elliptic functions is presented that approximates nonlinear dynamical systems with strong cubic nonlinearities in the presence of noise by a set of Itô differential equations. This is an extension of some recent results presented in deterministic dynamical systems. The second order nonlinear differential equation that is examined in this work can be expressed as % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWexLMBb50ujb% qeguuDJXwAKbacfiGaf8hEaGNbamaacqGHRaWkcaWGJbadcaaIXaGc% cqWF4baEcqGHRaWkcaWGJbadcaaIZaGccqWF4baEdaahaaWcbeqaai% aaiodaaaGccqGHRaWkcqaH1oqzcaWGMbGaaiikaiab-Hha4jaacYca% cqWFGaaicuWF4baEgaGaaiaacMcacqGHRaWkcqaH1oqzdaahaaWcbe% qaaiaaigdacaGGVaGaaGOmaaaaruWrL9MCNLwyaGGbcOGaa43zaiaa% cIcacqWF4baEcaGGSaGae8hiaaIaf8hEaGNbaiaacaGGSaGae8hiaa% IaeqOVdGNaaeikaiaadshacaqGPaGaaiykaiabg2da9iaaicdaaaa!645D![ddot x + c1x + c3x^3 + varepsilon f(x, dot x) + varepsilon ^{1/2} g(x, dot x, xi {text{(}}t{text{)}}) = 0] where c 1 and c 3 are given constants, ξ( t ) is stationary stochastic process with zero mean and ε≪1 is a small parameter. This method involves the laborious manipulation of Jacobian elliptic functions such as cn, dn and sn rather than the usual trigonometric functions. The use of a symbolic language such as Mathematica reduces the computational effort and allows us to express the results in a convenient form. The resulting equations are Markov approximations of amplitude and phase involving integrals of elliptic functions. Finally, this method was applied to study some standard second order systems.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43328/1/11071_2004_Article_BF00120672.pd

Almost-sure stability of a gyropendulum subjected to white-noise random support motion

Instability behaviour of a gyropendulum subjected to white noise vertical support motion is examined. Conditions for almost-sure asymptotic stability are obtained explicitly. A stochastic averaging procedure is employed to evaluate the maximal Lyapunov exponent. The sign of this exponent determines the instability behaviour of this system. Closed-form expressions for the instability conditions obtained in this study are employed to predict the minimum level of damping required to ensure almost-sure asymptotic stability. (C) 2000 Academic Press

The Application of Blockchain Technology to Smart City Infrastructure

A smart city can be defined as an integration of systems comprising a plethora of task-oriented technologies that aim to evolve and advance with city and infrastructure needs while providing services to citizens and resolving urban challenges through intersystem and data-driven analytical means, with minimal human intervention. Applications of technology include management, operations, and finance. One such technology is Blockchain. A main advantage of Blockchain is the simplification of processes that are costly and time-consuming. This is accomplished by simplifying operations to minimize costs resulting from the decentralization of assets. Blockchain has been proven to facilitate transparency, security, and the elimination of data fragmentation. However, as a relatively new technology, it poses regulatory obstacles. This issue can be attributed to the fact that many infrastructural governing organizations have incomplete knowledge of their infrastructure, which can lead to confusion when attempting to comprehend the different elements of the infrastructure, resulting in a lack of direction when trying to solve a problem. This paper explores the different applications of Blockchain technology in the sectors of energy, transportation, water, construction, and government, and provides a mechanism for implementing this technology in smart cities. As a present component of infrastructure management systems, Blockchain may potentially serve as the initial step toward upgrading infrastructure technology