Bifurcation analysis in a predator-prey system with stage-structure and harvesting

In this paper, we consider a predator-prey model with stage-structure and harvesting. This model is the same as the one developed by Kar and Pahari (2007) [9], but we make bifurcation analysis more general than their work. In particular, using the approach of Beretta and Kuang (2002) [4], we show that the positive steady state can be destabilized through a Hopf bifurcation. We also investigate the stability and direction of periodic solutions bifurcating from Hopf bifurcation by using the normal form theory and the center manifold theorem presented in Hassard et al. (1981) [8]. Numerical simulations are then carried out as supporting evidences of our analytical results.     

Sliding mode control for active magnetic bearing system with flexible rotor

This paper presents the analysis and control of active magnetic bearing (AMB) systems with a flexible rotor. A sliding mode controller design scheme is proposed to compensate for the nonlinear effects of the AMB system. A nonlinear model of the AMB system with an electromagnetic actuator and a flexible rotor is proposed to facilitate the present system analysis and controller design. This nonlinear model takes into account the dynamics of the flexible rotor, the characteristics of the nonlinear electromagnetic suspended system, and the contact force between the auxiliary bearing and the shaft. This study also considers the auto-centering control of the AMB system when subjected to disturbances and variations in the system parameters. The numerical results show that the system exhibits a periodic motion and demonstrates high accuracy and robustness when operating under sliding mode control.     

Bifurcation analysis and control of a discrete harvested prey-predator system with Beddington-DeAngelis functional response

In this paper, we study a discrete prey-predator system with harvesting of both species and Beddington-DeAngelis functional response. By using the center manifold theorem and bifurcation theory, we establish that the system undergoes flip bifurcation and Hopf bifurcation when the harvesting effort of prey population passes some critical values. Numerical simulations exhibit period-6, 10, 12, 14, 20 orbits, cascade of period-doubling bifurcation in period-2, 4, 8, 16 orbits and chaotic sets. At the same time, the numerically computed Lyapunov exponents confirm the complex dynamical behaviors. Moreover, a state delayed feedback control method, which can be implemented only by adjusting the harvesting effort for the prey population, is proposed to drive the discrete prey-predator system to a steady state.     

Bifurcation analysis of a competitive system with general toxic production and delayed toxic effects

Population interaction may release poisonous chemicals to inhibit other species’ growth in the ecosystem, especially for the competitive populations. The negative effect of toxic chemical substances may not display immediately and appear with time lag during the species’ growth. In this work, we investigate a competitive system with the delayed toxic effects of the chemicals from species interaction. Theoretical results obtained in this work help us reveal the delayed toxic factors on species’ growth. We first consider the existence and the stability of the equilibria. The influence of delay terms on the positive steady state is validated. The delayed toxic effects here will contribute to the oscillation for the concentration of species when the value of time delay passes through a critical point. Besides, the stability of periodic solutions from the Hopf bifurcation and the direction of the Hopf bifurcation are also determined. Finally, several numerical examples are provided to validate the theoretical conclusions.     

On dynamics analysis of a novel three-scroll chaotic attractor

This paper reports a novel chaotic member to the three-dimensional smooth autonomous quadratic system family, which is derived from the classical Chen system but exhibits a three-scroll chaotic attractor. The basic dynamical properties, such as Lyapunov exponents, fractal dimension, Poincaré map and chaotic dynamical behaviors of the new chaotic system are studied, either numerically or analytically. Simulation results clearly show that this is a novel chaotic system and deserves further detailed investigation.     

Bifurcation and control of a planktonic ecological system with double delays by delayed feedback control

In this paper, a delayed feedback controller with the delay-dependent coefficient is introduced into a multiple delay phytoplankton-zooplankton system. For uncontrolled system, choosing delays as the bifurcation parameters, we prove that Hopf bifurcation can occur when the delays change and cross some values. Then, the delays are still chosen as the bifurcation parameters to research the dynamic behaviors of the controlled system. Under this control mechanism, the onset of Hopf bifurcation can be delayed by selecting the appropriate control parameters and the stability domain can be extended as feedback gain (the decay rate) decreases (increases), and the influence of the decay rate cannot be ignored. Furthermore, using the crossing curve methods, the stable changes of equilibrium in two delay plane can be obtained. Some numerical simulations are given to verify the correctness and validity of the delayed feedback controller in the bifurcation control.     

混沌序列变换成均匀伪随机序列的普适算法的FPGA实现

针对现有的PRNG的均匀性差的特性,文献[1]提出了一种将混沌序列变换成均匀伪随机序列的普适算法。我们首次提出该算法的FPGA实现方案,方案由上位机软件、UART控制器、初值缓存器、均匀化算法实现单元、尾数序列缓存转换器组成。采用VHDL完成各模块设计,芯片选用逻辑资源为100万门的CycloneIIEP2C35F672C6,硬件电路共占6721逻辑单元,资源率20%,工作频率为50MHz。     

一类电力系统分岔的仿真研究

本文为了研究一类经典二维非线性电力系统的分岔现象,介绍了电力系统模型中常见分岔的基本概念,求出系统产生鞍结分岔的条件。利用MATLAB软件对此电力系统的分岔现象进行了数值仿真研究。文中给出了不同参数变化时系统的状态响应曲线。仿真分析验证了鞍结分岔产生的条件,同时直观给出参数变化对电力系统的分岔影响。结论表明,系统的参数变化都会引起系统状态的分岔现象。参数E和参数V随着数值的增大,系统复杂性增加,最后导致混沌,而机械输入功率Pm的变化会引起更复杂的动力学行为,出现周期性的分岔和混沌现象,所以在实际电力系统的运转中要注意对此参数的控制。     

Bifurcation with regard to combined interaction parameter in a life energy system dynamic model of two components with multiple delays

Bifurcation theory is commonly used to study the dynamical behavior of ecosystems. It involves the analysis of points in the parameter space where the stability of the system changes qualitatively. The type of bifurcation that associates equilibria with periodic solution is called Hopf bifurcation. In this paper, a life energy system dynamic model of two components with multiple delays is presented. It is shown that the interaction parameters of the delayed ecosystem play a fundamental role in classifying the rich dynamics and bifurcation phenomena. Regarding the combined interaction parameter as a bifurcation parameter, the bifurcation values in the parameter plane are displayed. The direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by applying the normal form theory and the center manifold theorem. Moreover, the amplitudes of oscillations always increase as the interaction parameters increase, while the robustness of periods occurs as the interaction parameters vary. From an ecological point of view, the existence of Hopf bifurcation expresses periodic oscillatory behavior of the life energy system.     

Propagation of projective synchronization in a series connection of chaotic systems

Projective synchronization is a type of chaos synchronization where the response system states are scaled replicas of the drive system states. This paper deals with the propagation of projective synchronization in a series connection of N chaotic discrete-time drive systems and N response systems. By exploiting an observer-based approach, the paper demonstrates that dead-beat projective synchronization (i.e., exact synchronization in finite time for any scaling factor) is achieved between the nth drive and nth response systems. In particular, it is shown that projective synchronization starts from the innermost (Nth) drive-response system pair and propagates toward the outermost (first) drive-response system pair. Only a single scalar synchronizing signal connects the cascaded drive and response systems. Finally, an example illustrates the propagation of different types of chaos synchronization in a series connection consisting of a Gingerbreadman map, a third order hyperchaotic Henon map and a Lozi map.     

浅谈混沌通信

本文介绍了基于混沌理论的通信技术,包括混沌掩盖技术、混沌码分多址技术及混沌扩频技术、混沌通信系统中的同步的发展现状等等。     

VCO sweep-rate limit for a phase-lock loop

Phase-lock loops (PLLs) serve important roles in phase-lock receivers, coherent transponders, and similar applications. For many of these uses, the bandwidth of the loop must be kept small to limit the detrimental influence of noise, and this requirement makes the natural PLL pull-in phenomenon too slow and/or unreliable. For each such case, the phase-lock acquisition process can be aided by the application of an external sweep voltage to the loop voltage controlled oscillators (VCOs). The goal is to have the applied sweep voltage rapidly decrease the closed-loop frequency error to a point where phase lock occurs quickly. For a second-order loop containing a perfect integrator loop filter, there is a maximum VCO sweep-rate magnitude, denoted here as R_m rad/s², for which phase lock is guaranteed. If the applied VCO sweep rate is less than R_m, the loop cannot sweep past a stable phase-lock point, and it will phase lock. On the other hand, for an applied sweep-rate magnitude that is greater than R_m, the PLL may sweep past a lock point and fail to phase lock. In the existing PLL literature, only a trial-and-error approach has been described for estimating R_m, given values of loop damping factor ζ and natural frequency ω_n. Furthermore, no plots exist of computed versus ζ and versus ζ (B_L denotes loop-noise bandwidth). These deficiencies are dealt with in this paper. A new iterative numerical technique is given that converges to the maximum sweep-rate magnitude R_m. It is used to generate data for plots of and versus ζ, the likes of which have never appeared before in the PLL literature.     

Migration distance-based platelet function analysis in a microfluidic system

Aggregation and adhesion of platelets to the vascular wall are shear-dependent processes that play critical roles in hemostasis and thrombosis at vascular injury sites. In this study, we designed a simple and rapid assay of platelet aggregation and adhesion in a microfluidic system. A shearing mechanism using a rotating stirrer provided adjustable shear rate and shearing time and induced platelet activation. When sheared blood was driven through the microchannel under vacuum pressure, shear-activated platelets adhered to a collagen-coated surface, causing blood flow to significantly slow and eventually stop. To measure platelet adhesion and aggregation, the migration distance (MD) of blood through the microchannel was monitored. As the microstirrer speed increased, MD initially decreased exponentially but then increased beyond a critical rpm. For platelet-excluded blood samples, there were no changes in MD with increasing stirrer speed. These findings imply that the stirrer provided sufficiently high shear to activate platelets and that blood MD is a potentially valuable index for measuring the shear-dependence of platelet activation. Our microfluidic system is quick and simple, while providing a precise assay to measure the effects of shear on platelet aggregation and adhesion.     

Dynamical behavior in a harvested differential-algebraic prey-predator model with discrete time delay and stage structure

A differential-algebraic model system which considers a prey-predator system with stage structure for prey and harvest effort on predator is proposed. By using the differential-algebraic system theory and bifurcation theory, the dynamic behaviors of the proposed model system with and without discrete time delay are investigated. Local stability analysis of the model system without discrete time delay reveals that there is a phenomenon of singularity induced bifurcation due to variation of the economic interest of harvesting, and a state feedback controller is designed to stabilize the proposed model system at the interior equilibrium; on the other hand, the local stability of the model system with discrete time delay is also studied. The theoretical analysis shows that the discrete time delay has a destabilizing effect in the model of population dynamics, and a phenomenon of Hopf bifurcation occurs as the discrete time delay increases through a certain threshold. Numerical simulations are carried out to show the consistency with theoretical analysis.     

多热源分布时薄层液体中热毛细对流的分叉特征

本文研究一个液体薄层在热源作用下的流动特征。Pimputakar和Ostrach给出了单热源作用下薄层液体的高度和流场方程。本文在此基础上具体分析比较了多个热源分布作用下的流动图象随各参数尤其是随热源间距离不同的变化情况，着重讨论产生的分叉现象。     

一类参数激励非线性振子的周期分岔序列和混沌行为

用数值方法对一类参数激励的非线性DUffing-Van der Pol振子进行了研究.着重考察了系统随周期驱动力角频率ω改变的周期分岔序列及混沌行为.给出了各种振荡态和混沌态随时间的循环模式.发现在一定的ω值区间内,周期运动和混沌运动交替出现,周期运动会失稳直接进入混沌态.对通向混沌的道路问题也作了一些探讨.     

汽轮机调节系统工作不稳定分析

调节系统的不稳定影响汽轮机的生产稳定性，同时给机组的安全运行也带来了不利因素。针对汽轮机调节系统工作不稳定的情况，对其进行了理论的分析，总结归纳了影响汽轮机调节系统工作稳定的各种原因，及其处理措施。     

汽轮机调节系统工作不稳定分析

调节系统的不稳定影响汽轮机的生产稳定性,同时给机组的安全运行也带来了不利因素。针对汽轮机调节系统工作不稳定的情况,对其进行了理论的分析,总结归纳了影响汽轮机调节系统工作稳定的各种原因,及其处理措施。     

Stability analysis of a rotor-AMB system with time varying stiffness

A rotor-active magnetic bearing (AMB) system subjected to a periodically time-varying stiffness with quadratic and cubic nonlinear under tuned, and external excitation is studied. The method of multiple scales is applied to analyze the response of two modes of a rotor-AMB system near the simultaneous combined and sub-harmonic resonance. The stability of the steady-state solution for that resonance is determined and studied applying Rung–Kutta fourth order method. It is shown that the system exhibits many typical nonlinear behaviors, including multiple-valued solutions, jump phenomenon, hardening and softening nonlinear and chaos in the second mode of the system. The effects of the different parameters on the steady-state solutions are investigated and discussed.