A general theory of phase noise in electrical oscillators

A general model is introduced which is capable of making accurate, quantitative predictions about the phase noise of different types of electrical oscillators by acknowledging the true periodically time-varying nature of all oscillators. This new approach also elucidates several previously unknown design criteria for reducing close-in phase noise by identifying the mechanisms by which intrinsic device noise and external noise sources contribute to the total phase noise. In particular, it explains the details of how 1/f noise in a device upconverts into close-in phase noise and identifies methods to suppress this upconversion. The theory also naturally accommodates cyclostationary noise sources, leading to additional important design insights. The model reduces to previously available phase noise models as special cases. Excellent agreement among theory, simulations, and measurements is observed

Oscillation for solutions of nonlinear neutral differential equations with impulses

AbstractThis paper is concerned with nonlinear neutral differential equations with impulses of the form Some oscillation criteria for solutions of this equation are established. An interesting example is also given, which illustrates that impulses play an important role in giving rise to the oscillation of equations

Spike-Train Responses of a Pair of Hodgkin-Huxley Neurons with Time-Delayed Couplings

Model calculations have been performed on the spike-train response of a pair of Hodgkin-Huxley (HH) neurons coupled by recurrent excitatory-excitatory couplings with time delay. The coupled, excitable HH neurons are assumed to receive the two kinds of spike-train inputs: the transient input consisting of $M$ impulses for the finite duration ($M$: integer) and the sequential input with the constant interspike interval (ISI). The distribution of the output ISI $T_{\rm o}$ shows a rich of variety depending on the coupling strength and the time delay. The comparison is made between the dependence of the output ISI for the transient inputs and that for the sequential inputs.Comment: 19 pages, 4 figure

Oscillatory criteria for Third-Order difference equation with impulses

AbstractIn this paper, we investigate the oscillation of Third-order difference equation with impulses. Some sufficient conditions for the oscillatory behavior of the solutions of Third-order impulsive difference equations are obtained

Oscillation of second order self-conjugate differential equation with impulses

AbstractIn this paper, we investigate the oscillation of second-order self-conjugate differential equation with impulses(1)(a(t)(x(t)+p(t)x(t-τ))′)′+q(t)x(t-σ)=0,t≠tk,t⩾t0,(2)x(tk+)=(1+bk)x(tk),k=1,2,…,(3)x′(tk+)=(1+bk)x′(tk),k=1,2,…,where a,p,q are continuous functions in [t0,+∞), q(t)⩾0, a(t)>0, ∫t0∞(1/a(s))ds=∞, τ>0, σ>0, bk>-1, 0<t0<t1 <t2<⋯<tk<⋯ and limk→∞tk=∞. We get some sufficient conditions for the oscillation of solutions of Eqs. (1)–(3)

Invariant and attracting sets of impulsive delay difference equations with continuous variables

AbstractThe aim of this paper is to study the invariant and attracting sets of impulsive delay difference equations with continuous variables. Some criteria for the invariant and attracting sets are obtained by using the decomposition approach and delay difference inequalities with impulsive initial conditions

Oscillation of third order Impulsive Differential Equations with delay

This paper deals with the oscillation of third order impulsive differential equations with delay. The results of this paper improve and extend some&nbsp;results for the differential equations without impulses. Some examples are givento illustrate the main results

Positive periodic solutions generated by impulses for the delay Nicholson's blowflies model

In this paper, by using Krasnoselskii's fixed point theorem, we study the existence and multiplicity of positive periodic solutions for the delay Nicholson's blowflies model with impulsive effects. Our results show that these positive periodic solutions are generated by impulses. To the authors' knowledge, there are no papers about positive periodic solution generated by impulses for first order delay differential equation. Our results are completely new. Finally, some examples are given to illustrate our main results

Asymptotic Dichotomy in a Class of Third-Order Nonlinear Differential Equations with Impulses

Solutions of quite a few higher-order delay functional differential equations oscillate or converge to zero. In this paper, we obtain several such dichotomous criteria for a class of third-order nonlinear differential equation with impulses