This paper addresses the amplitude and phase dynamics of a large system of nonlinearly coupled, non-identical damped harmonic oscillators, which is based on recent research in coupled oscillation in optomechanics. Our goal is to investigate the existence and stability of collective behaviour which occurs due to a play-off between the distribution of individual oscillator frequency and the type ...

11.1 Introduction Spiking neurons are highly non-linear oscillators. As such they display collective behavior that may have important calculational manifestations. Synchronization between the ring of diierent neurons is the rst topic to which we devote our attention. This behavior can be brought about in our integrate-and-re model through excita-tory synaptic couplings without delays, or inhibi...

In this paper, we present a numerical scheme using uniform Haar wavelet approximation and quasilinearization process for solving some nonlinear oscillator equations. In our proposed work, quasilinearization technique is first applied through Haar wavelets to convert a nonlinear differential equation into a set of linear algebraic equations. Finally, to demonstrate the validity of the proposed m...

Unlike conservative oscillatory media, dissipative self-oscillatory media admit traveling waves without decay even in the presence of noise or other sources of randomness. This ability of wave transmission in random self-oscillatory media should be functionally relevant in a variety of living organisms for which randomness is unavoidable. For this type of systems, a critical strength of randomn...

The concept of spin-torque-driven high-frequency magnetization dynamics, allows the potential construction of complex networks of non-linear dynamical nanoscale systems, combining the field of spintronics and the study of non-linear systems. In the few previous demonstrations of synchronization of several spin-torque oscillators, the short-range nature of the magnetic coupling that was used has...

The “standard” Brownian motion master equation, used to describe thermal damping, is not completely positive, and does not admit a Monte Carlo method, important in numerical simulations. To eliminate both these problems one must add a term that generates additional position diffusion. He we show that one can obtain a completely positive simple quantum Brownian motion, efficiently solvable, with...

We present the Girsanov theorem for a non linear Itô equation in an infinite dimensional Hilbert space with a non linearity of polynomial growth and an infinite dimensional additive noise. We assume a condition weaker than Novikov one, as done by Mikulevicius and Rozovskii in the study of more general stochastic PDE’s. The equivalence of the laws of the linear equation and of the non linear equ...

It is well known that an autonomous dynamical system can have a stable periodic orbit, arising for example through a Hopf bifurcation. When a collection of such oscillators is coupled together, the system can display a number of phase-locked solutions which can be understood in the weak coupling limit by using a phase model. It is also well known that a stable periodic orbit can be found for a ...