Numerical Continuation and Bifurcation Analysis in a Harvested Predator-Prey Model with Time Delay using DDE-Biftool

Time delay has been incorporated in models to reflect certain physical or biological meaning. The theory of delay differential equations (DDEs), which has seen extensive growth in the last seventy years or so, can be used to examine the effects of time delay in the dynamical behavior of systems being considered. Numerical tools to study DDEs have played a significant role not only in illustrating theoretical results but also in discovering interesting dynamics of the model. DDE-Biftool, which is a Matlab package for numerical continuation and numerical bifurcation analysis of DDEs, is one of the most utilized and popular numerical tools for DDEs. In this paper, we present a guide to using the latest version of DDE-Biftool targeted to researchers who are new to the study of time delay systems. A short discussion of an example application, which is a harvested predator-prey model with a single discrete time delay, will be presented first. We then implement this example model in DDE-Biftool, pointing out features where beginners need to be cautious. We end with a comparison of our theoretical and numerical results

Wearable electromagnetic head imaging system using flexible wideband antenna array based on polymer technology for brain stroke diagnosis

Given the increased interest in a fast, portable, and on-spot medical diagnostic tool that enables early diagnosis for patients with brain stroke, a new approach of a wearable electromagnetic head imaging system based on the polymer material is proposed. A flexible low-profile, wideband, and unidirectional antenna array with electromagnetic band gap (EBG) and metamaterial (MTM) unit cells reflector is utilized. The designed antenna consists of a 4 x 4 radiating patch loaded with symmetrical extended open-ended U-slots and fed by combination of series and corporate transmission lines. A mushroom-like 10-EBG unit cell arrays are arranged around the feeding network to reduce surface waves, whereas 4 x 4 MTM unit cells are placed on the back-side of the antenna to enable unidirectional radiation. The antenna is designed and embedded on a multilayer low cost, low loss, transparent, and robust polymer poly-di-methyl-siloxane (PDMS) substrate and optimized to operate in contact with the human head. The simulated and measured results show that the antenna has a fractional bandwidth of 53.8% (1.16-1.94 GHz), more than 80% of radiation efficiency, and satisfactory field penetration in the head tissues with a safe specific absorption rate. An eight-element array is then configured on 300 x 360 x 4.1 mm(3) PDMS material covering an average human head size and used as a worn part of the imaging system. A realistic-shaped 3-D specific anthropomorphic mannequin (SAM) head phantom is used to verify the performance of the designed array. The imaging results indicate the possibility of using the designed conformal array to detect a bleeding inside the brain using a confocal image algorithm

Stability analysis rabies model in animals with the effect of vaccination and sterilization

A deterministic model for the transmission dynamics of the rabies virus in animals is formulated. The effect of rabies vaccine, surgical sterilization and rabies immuno-contraceptive vaccine is considered in the model, then the stability of the disease-free equlilibrium is analyzed to get the basic reproduction number using the next generation matrix method. Both local stability and global stability of the model are analyzed and written down as theorems

Design of compact cross-fed three-dimensional slot-loaded antenna and its application in wideband head imaging system

Microwave head imaging systems require compact wideband antennas with directional radiation. To realize the antenna miniaturization, the halving technique based on image theory has been used. However, it causes a tilt in the main-beam direction. This letter demonstrates that the side feeding technique can be used to cross-feed the halved antennas with the potential to retain their beam direction. The performances of one-sided direct-feeding and cross-feeding methods are compared using a halved slot-loaded folded-dipole antenna. The underlying mechanism behind the beam correction is analyzed. The prototyped antenna achieves 97% fractional bandwidth (1.1-3.2 GHz) and an average gain of 3 dBi along its boresight direction. The overall dimensions of the designed antenna (with respect to the lowest operating wavelength) are 0.25 × 0.06 × 0.06 λ . The measured near- and far-field radiation patterns demonstrate the unidirectional radiation of the antenna with a stable boresight main beam. Moreover, considering the fundamental limit of antennas, the prototyped antenna is found to be near the edge of optimally attainable solutions. The antenna is applied in an automated microwave head imaging system. The reconstructed images illustrate the efficacy of increasing sensing elements, due to antenna compactness, to detect hemorrhagic strokes inside a realistic artificial human head