Analysis of Effects of Delays and Diffusion on a Predator-Prey System

A reaction-diffusion predator-prey system with two delays is investigated. It is found that the spatially homogeneous periodic solution will occur when the sum of two delays crosses some critical values and Hopf bifurcation takes place. For the fixed domain and diffusion, some numerical simulations are also given to illustrate the theoretical analysis. In addition, special attention is paid to effects of diffusion on the bifurcating periodic solution. It is found that the diffusion would lead to the bifurcating period solution to destabilize by calculating the relevant expression of the Floquet exponent.

Stability and Bifurcation in Magnetic Flux Feedback Maglev Control System

Nonlinear properties of magnetic flux feedback control system have been investigated mainly in this paper. We analyzed the influence of magnetic flux feedback control system on control property by time delay and interfering signal of acceleration. First of all, we have established maglev nonlinear model based on magnetic flux feedback and then discussed hopf bifurcation’s condition caused by the acceleration’s time delay. The critical value of delayed time is obtained. It is proved that the period solution exists in maglev control system and the stable condition has been got. We obtained the characteristic values by employing center manifold reduction theory and normal form method, which represent separately the direction of hopf bifurcation, the stability of the period solution, and the period of the period motion. Subsequently, we discussed the influence maglev system on stability of by acceleration’s interfering signal and obtained the stable domain of interfering signal. Some experiments have been done on CMS04 maglev vehicle of National University of Defense Technology (NUDT) in Tangshan city. The results of experiments demonstrate that viewpoints of this paper are correct and scientific. When time lag reaches the critical value, maglev system will produce a supercritical hopf bifurcation which may cause unstable period motion.

Stability and Permanence of a Pest Management Model with Impulsive Releasing and Harvesting

We formulate a pest management model with periodically releasing infective pests, immature and mature natural enemies, and harvesting pests and crops at two different fixed moments. Sufficient conditions ensuring the locally and globally asymptotical stability of the susceptible pest-eradication period solution are found by means of Floquet theory, small amplitude perturbation techniques, and multicomparison results. Furthermore, the permanence of system is also derived. By numerical analysis, we also show that impulsive releasing and harvesting at two different fixed moments can bring obvious effects on the dynamics of system, which also corroborates our theoretical results.

Hopf Bifurcation for a Model of HIV Infection ofCD4+T Cells with Virus Released Delay

A viral model of HIV infection ofCD4+T-cells with virus released period is formulated, and the effect of this released period on the stability of the equilibria is investigated. It is shown that the introduction of the viral released period can destabilize the system, and the period solution may arise. The direction and stability of the Hopf bifurcation are also discussed. Numerical simulations are presented to illustrate the results.

Employing A Tax Practitioner: A Different Perspective

<p class="MsoBlockText" style="margin: 0in 32.6pt 0pt 0.5in;"><span style="font-size: 10pt; mso-bidi-font-family: 'Times New Roman'; mso-no-proof: no;"><span style="font-family: Times New Roman;">In this paper, we analyze the value of services rendered by tax practitioners,<span dir="rtl"> </span>demonstrating that the conventional single-period solution may be inconsistent with their role. We contend that the value of these services stems from tax practitioners' knowledge of the tax code and not from the signal they convey to tax authorities when they sign the returns. We take the position that taxpayers' actions may not convey a signal to the tax enforcement agent, thereby enabling the latter to set different detection rates for different taxpayers. If taxpayers' actions were to convey a signal, the solution would not be sustainable, since it would eventually lead to a self-revealing &ldquo;corner solution,&rdquo; in which all taxpayers would take the same action. </span></span></p><p class="MsoNormal" style="text-align: justify; margin: 0in 32.6pt 0pt 0.5in; unicode-bidi: embed; direction: ltr;"><span style="mso-bidi-font-family: 'Times New Roman'; mso-no-proof: no;"><span style="font-family: Times New Roman; font-size: x-small;">&nbsp;</span></span></p><p class="MsoNormal" style="text-align: justify; margin: 0in 32.6pt 0pt 0.5in; unicode-bidi: embed; direction: ltr;"><span style="mso-bidi-font-family: 'Times New Roman'; mso-no-proof: no;"><span style="font-size: x-small;"><span style="font-family: Times New Roman;">In a single-period framework, the taxpayer&rsquo;s decision to hire a practitioner is dependent upon two variables: the practitioners&rsquo; fee, which is known to the tax enforcement agent, and taxpayers' risk attitude. The tax enforcement agent can infer the latter if the taxpayers use practitioners who sign the tax returns.<span style="mso-spacerun: yes;">&nbsp; </span>If taxpayers use practitioners&rsquo; services, we are able to derive the same exact solution irrespective of whether or not practitioners<strong> </strong>sign the returns.<span style="mso-spacerun: yes;">&nbsp; </span>Thus, we suspect that the value of these services does not stem from the fact that the returns are signed. </span></span></span></p>

THE OPTIMAL PULSE HARVESTING POLICY ON A SINGLE-SPECIES POPULATION MODEL WITH BIRTH PULSES IN A POLLUTED ENVIRONMENT

We investigate the dynamics of a single-species model with birth pulses and pulse harvesting in a polluted environment. Using the discrete dynamical system determined by the stroboscopic map, we obtain an exact 1-period solution of the system whose birth function is a Ricker or Beverton–Holt function and obtain the threshold conditions for their stability. Further, we show the effects of the time of pulse harvesting on the maximum annual-sustainable yield. Our results show that the best time for harvesting is immediately after the birth pulses. Numerical simulation results also show that birth pulses and pulse harvesting make the single-species model in a polluted environment we consider more complex, and the system is dominated by periodic and chaotic solutions.

Fundamental Periods of Vibration of Braced Steel Frames for Seismic Design

An analytical study is performed to propose a simple expression for the fundamental period of vibration of concentrically braced steel frames. This work was carried out in the context of the development of the 2005 National Building Code of Canada (NBCC) and is mainly applicable to structures located in moderate and low seismic regions. Available field and test measurements of building periods are compared to analytical predictions. An empirical period formula is developed based on a survey of analytically computed building periods published in the literature. The influence of the 2005 NBCC design provisions on braced steel-frame periods is examined through a closed-form period solution and an extensive parametric study. Building periods are found to vary significantly with seismic hazard levels and soil conditions. An expression is tentatively proposed that provides reasonable lower-bound period estimates for most situations in Canada.