Multidimensional linear hyperbolic systems with constraints and delay are considered. The existence and uniqueness of solutions for rough data are established using Friedrichs method. With additional regularity and compatibility on the initial data and initial history, the stability of such systems are discussed. Under suitable assumptions on the coefficient matrices, we establish standard or regularity-loss type decay estimates. For data that are integrable, better decay rates are provided. The results are applied to the wave, Timoshenko, and linearized Euler–Maxwell systems with delay.

We study a fractional-order delayed predator-prey model with Holling–Tanner-type functional response. Mainly, by choosing the delay time $\tau $ as the bifurcation parameter, we show that Hopf bifurcation can occur as the delay time $\tau $ passes some critical values. The local stability of a positive equilibrium and the existence of the Hopf bifurcations are established, and numerical simulations for justifying the theoretical analysis are also presented.

The phase error in a high quality accelerometer was investigated on the basis of systematic experiments on a prototype platform permitting controlled vertical harmonic oscillations. The recordings of an accelerometer and of an ultra-high frequency GPS fixed on this platform were compared with those of a LVDT transducer, controlling the platform movement. All sensors were supported by independent GPS timing. The output of this study is that the recordings of accelerometers are characterized by a random phase error, which, however, decreases with the increase of the oscillation frequency, as dictated from the laws of mechanics. Such errors are important given the increasing use of combinations of accelerometers with various sensors for a wide range of applications. A simple method for the correction of such errors is proposed.

The question, how does an organism maintain balance? provides a unifying theme tointroduce undergraduate students to the use of mathematics and modeling techniques inbiological research. The availability of inexpensive high speed motion capture camerasmakes it possible to collect the precise and reliable data that facilitates thedevelopment of relevant mathematical models. An in–house laboratory component ensures thatstudents have the opportunity to directly compare prediction to observation and motivatesthe development of projects that push the boundaries of the subject. The projects, bytheir nature, readily lend themselves to the formation of inter–disciplinary studentresearch teams. Thus students have the opportunity to learn skills essential for successin today’s workplace including productive team work, critical thinking, problem solving,project management, and effective communication.

In this work we study the optimal control problem for a class of nonlinear time-delaysystems via paratingent equation with delayed argument. We use an equivalence theorembetween solutions of differential inclusions with time-delay and solutions of paratingentequations with delayed argument. We study the problem of optimal control which minimizes acertain cost function. To show the existence of optimal control, we use the maintopological properties of the set solutions of paratingent equation with delayedargument

Increased speed of inverse dynamics computation is essential for improving the characteristics of robot control systems. This is achieved by reducing the numerical complexity of the models and by introducing parallelism in model computation. In this paper customized symbolic models with a near minimum numerical complexity will be used as a basis for the examination of parallelism in inverse dynamic robot models. A scheduling algorithm for the distribution of computational load onto an arbitrary linear array of pipelined processors will be developed. The proposed algorithm is experimentally evaluated on a transputer network.

Nowadays there has been a growing consciousness among the tea industry to reducethe use of the chemical pesticides for pest control. Predators are beneficial insects that feed onharmful insects and mites, which incur considerable loss of production of tea. In this paper wehave considered a tritrophic model consisting of tea plant, pest and predator to analyze differentfield observations. The effect of discrete time-delay on the tritrophic model is studied critically.The dynamical behaviours are studied both analytically and numerically by computer simulation.Our results suggest some theoretical measures which may be implemented for successful biologicalcontrol.