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Yongkun Li

Publications and source records attributed to Yongkun Li.

29 records · Page 2Linked to original sources
arXiv2016

Asymptotical stability of almost periodic solution for an impulsive multispecies competition-predation system with time delays on time scales

In this paper, we consider the almost periodic dynamics of an impulsive multispecies Lotka-Volterra competition system with time delays on time scales. By establishing some comparison theorems of dynamic equations with impulses and delays on time scales, a permanence result for the model is obtained. Furthermore, based on the permanence result, by studying the Lyapunov stability theory of impulsive dynamic equations on time scales, we establish a criterion for the existence and uniformly asymptotic stability of a unique positive almost periodic solution of the system. Finally, we give an example to show the feasibility of our main results and our example also shows that the continuous time system and its corresponding discrete time system have the same dynamics. Our results of this paper are completely new even if for both the case of the time scale $\mathbb{T}=\mathbb{R}$ and the case of $\mathbb{Z}$.

math.CA↗
arXiv2015

Existence and exponential stability of positive almost periodic solution for Nicholson's blowflies models on time scales

In this paper, we first give a new definition of almost periodic time scales, two new definitions of almost periodic functions on time scales and investigate some basic properties of them. Then, as an application, by using the fixed point theorem in Banach space and the time scale calculus theory, we obtain some sufficient conditions for the existence and exponential stability of positive almost periodic solutions for a class of Nicholson's blowflies models on time scales. Finally, we present an illustrative example to show the effectiveness of obtained results. Our results show that under a simple condition the continuous-time Nicholson's blowflies models and their discrete-time analogue have the same dynamical behaviors.

math.CA↗
arXiv2015

Pseudo almost periodic solutions for neutral type high-order Hopfield neural networks with mixed time-varying delays and leakage delays on time scales

In this paper, a class of neutral type high-order Hopfield neural networks with mixed time-varying delays and leakage delays on time scales is proposed. Based on the exponential dichotomy of linear dynamic equations on time scales, Banach's fixed point theorem and the theory of calculus on time scales, some sufficient conditions are obtained for the existence and global exponential stability of pseudo almost periodic solutions for this class of neural networks. Our results are completely new. Finally, we present an example to illustrate our results are effective. Our example also shows that the continuous-time neural network and its discrete-time analogue have the same dynamical behaviors for the pseudo almost periodicity.

math.CA↗
arXiv2015

Permanence and almost periodic solutions for a single-species system with impulsive effects on time scales

In this paper, we first propose a single-species system with impulsive effects on time scales and by establishing some new comparison theorems of impulsive dynamic equations on time scales, we obtain sufficient conditions to guarantee the permanence of the system. Then we prove a Massera type theorem for impulsive dynamic equations on time scales and based on this theorem, we establish a criterion for the existence and uniformly asymptotic stability of unique positive almost periodic solution of the system. Finally, we give an example to show the feasibility of our main results. Our example also shows that the continuous time system and its corresponding discrete time system have the same dynamics. Our results of this paper are completely new.

math.DS↗
arXiv2015

Permanence and almost periodic solution of a multispecies Lotka-Volterra mutualism system with time varying delays on time scales

In this paper, we consider the almost periodic dynamics of a multispecies Lotka-Volterra mutualism system with time varying delays on time scales. By establishing some dynamic inequalities on time scales, a permanence result for the model is obtained. Furthermore, by means of the almost periodic functional hull theory on time scales and Lyapunov functional, some criteria are obtained for the existence, uniqueness and global attractivity of almost periodic solutions of the model. Our results complement and extend some scientific work in recent years. Finally, an example is given to illustrate the main results.

math.DS↗
arXiv2015

Weighted pseudo-almost periodic functions on time scales with applications to cellular neural networks with discrete delays

In this paper, we first propose a concept of weighted pseudo-almost periodic functions on time scales and study some basic properties of weighted pseudo-almost periodic functions on time scales. Then, we establish some results about the existence of weighted pseudo-almost periodic solutions to linear dynamic equations on time scales. Finally, as an application of our results, we study the existence and global exponential stability of weighted pseudo-almost periodic solutions for a class of cellular neural networks with discrete delays on time scales. The results of this paper are completely new.

math.CA↗
arXiv2015

Almost automorphic funtions on time scales and almost automorphic solutions to shunting inhibitory cellular neural networks on time scales

In this paper, we first propose a new concept of almost periodic time scales, a new definition of almost automorphic functions on almost periodic time scales, and study some their basic properties. Then we prove a result ensuring the existence of an almost automorphic solution for both the linear nonhomogeneous dynamic equation on time scales and its associated homogeneous equation, assuming that the associated homogeneous equation admits an exponential dichotomy. Finally, as an application of our results, we establish the existence and global exponential stability of almost automorphic solutions to a class of shunting inhibitory cellular neural networks with time-varying delays on time scales. Our results about the shunting inhibitory cellular neural network with time-varying delays on time scales are new even for the both cases of differential equations(the time scale $\mathbb{T}=\mathbb{R})$ and difference equations(the time scale $\mathbb{T}=\mathbb{Z})$.

math.DS↗
arXiv2014

Friends or Foes: Distributed and Randomized Algorithms to Determine Dishonest Recommenders in Online Social Networks

Viral marketing is becoming important due to the popularity of online social networks (OSNs). Companies may provide incentives (e.g., via free samples of a product) to a small group of users in an OSN, and these users provide recommendations to their friends, which eventually increases the overall sales of a given product. Nevertheless, this also opens a door for "malicious behaviors": dishonest users may intentionally give misleading recommendations to their friends so as to distort the normal sales distribution. In this paper, we propose a detection framework to identify dishonest users in OSNs. In particular, we present a set of fully distributed and randomized algorithms, and also quantify the performance of the algorithms by deriving probability of false positive, probability of false negative, and the distribution of number of detection rounds. Extensive simulations are also carried out to illustrate the impact of misleading recommendations and the effectiveness of our detection algorithms. The methodology we present here will enhance the security level of viral marketing in OSNs.

cs.SI↗
arXiv2013

Stochastic Analysis on RAID Reliability for Solid-State Drives

Solid-state drives (SSDs) have been widely deployed in desktops and data centers. However, SSDs suffer from bit errors, and the bit error rate is time dependent since it increases as an SSD wears down. Traditional storage systems mainly use parity-based RAID to provide reliability guarantees by striping redundancy across multiple devices, but the effectiveness of RAID in SSDs remains debatable as parity updates aggravate the wearing and bit error rates of SSDs. In particular, an open problem is that how different parity distributions over multiple devices, such as the even distribution suggested by conventional wisdom, or uneven distributions proposed in recent RAID schemes for SSDs, may influence the reliability of an SSD RAID array. To address this fundamental problem, we propose the first analytical model to quantify the reliability dynamics of an SSD RAID array. Specifically, we develop a "non-homogeneous" continuous time Markov chain model, and derive the transient reliability solution. We validate our model via trace-driven simulations and conduct numerical analysis to provide insights into the reliability dynamics of SSD RAID arrays under different parity distributions and subject to different bit error rates and array configurations. Designers can use our model to decide the appropriate parity distribution based on their reliability requirements.

cs.PF↗
arXiv2013

Stochastic Modeling of Large-Scale Solid-State Storage Systems: Analysis, Design Tradeoffs and Optimization

Solid state drives (SSDs) have seen wide deployment in mobiles, desktops, and data centers due to their high I/O performance and low energy consumption. As SSDs write data out-of-place, garbage collection (GC) is required to erase and reclaim space with invalid data. However, GC poses additional writes that hinder the I/O performance, while SSD blocks can only endure a finite number of erasures. Thus, there is a performance-durability tradeoff on the design space of GC. To characterize the optimal tradeoff, this paper formulates an analytical model that explores the full optimal design space of any GC algorithm. We first present a stochastic Markov chain model that captures the I/O dynamics of large-scale SSDs, and adapt the mean-field approach to derive the asymptotic steady-state performance. We further prove the model convergence and generalize the model for all types of workload. Inspired by this model, we propose a randomized greedy algorithm (RGA) that can operate along the optimal tradeoff curve with a tunable parameter. Using trace-driven simulation on DiskSim with SSD add-ons, we demonstrate how RGA can be parameterized to realize the performance-durability tradeoff.

cs.PF↗