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Dynamical Complexity of Patchy Invasion in Prey–Predator Model
Published in Mangey Ram, Recent Advances in Mathematics for Engineering, 2020
Formation of spatial patterns in nature is ubiquitous, with illustrations like zebra stripe patterns on animals skin, Turing patterns in a coherent quantum field, or diffusive patterns in predator-prey models [2,25,29]. The spatial factors of species interplay have been recognized as a vital component in how ecological communities are created and ecological interplay occurs over a broad limit of temporal and spatial scale [12]. Spatial population distribution is of major importance in the study of ecological systems [17,18,30]. Mechanisms and scenarios characterizing the spatial population distribution of ecological species in spatial habitat are a focus of special interest in population dynamics. The spatial population distribution is affected by the proliferation capacity of the species and interactions between individuals [35]. Spatial effect may be disregarded in a certain extent, particularly when the population of a given species stay fixed in space at any moment of time. Albeit this assumption is not completely realistic. Individuals of an ecological species do not fix at all times in space, and their dispersion in space changes incessantly by the self-movement of individuals [17,19,21,25,26].
Design of Reconfigurable Antenna Using MSF-EBG Structure to Improve Performance Parameters
Published in IETE Journal of Research, 2022
Manasi Shrikant Kanitkar, Shankar Baburao Deosarkar
The term fractal, which means broken or irregular frapents, was originally coined by Mandelbrot [1] to describe a family of complex shapes that possess an inherent self-similarity or self-affinity in their geometrical structure. The original inspiration for the development of fractal geometry came largely from an in-depth study of the patterns of nature. Since 1999, the electromagnetic band gap (EBG) structures have been investigated for improving performances of numerous RF and microwave devices utilizing the surface wave suppression and the racial magnetic conductor properties of different sections. These are special types of metamaterial. The concept of EBG structures originates from the solid-state physics and optic domain, where photonic crystals with forbidden band gap are used for light emissions. Thus, the terminology, photonic band gap structures, was popularly used in the early days [2]. The unique feature of EBG structure is the existence of the band gap where electromagnetic waves are not allowed to propagate certain frequency bands at microwave or millimeter-wave frequencies.
Assessment of Scale Invariance Changes in Heart Rate Signal During Postural Shift
Published in IETE Journal of Research, 2022
Helen M. C. Mary, Dilbag Singh, K. K. Deepak
Fractal analysis is a nonlinear mathematical method derived from fractal geometry [6–7]. A fractal is a mathematical set that has a fractal dimension that usually exceeds its topological dimension and may fall between the integers. A fractal is defined as “a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,” a property called self-similarity/scale invariance [8]. The notion of fractals was introduced by Benoit Mandelbrot in 1975. The term fractal derived from the Latin word fractus means “break into pieces” [6]. The classic example of a natural fractal object is the coastline. In the beginning of the twentieth century, Richardson, the English hydro mechanical engineer, faced certain difficulties when he tried to measure the length of the Great Britain coastline. He tried to substitute the coastline by the broken line. It turned out that when the scale was decreased, the calculated length of the broken line increased greatly. Mandelbrot offered to apply the law of power dependence to approximate the degree of the increase of the coastline length. Most objects in nature are not formed of definite shapes like squares or triangles, but of more complicated geometric figures. Euclidean described only about regular shapes like line, rectangle, square, … etc. but to analyze irregular shapes like time series, … etc., we need fractal geometry. These irregular shapes cannot be approximated as regular shapes. Fractals used to extend the concept of theoretical fractional dimensions to geometric patterns in nature. To measure the length of a fractal (self-similar object) is more useful to determine the power law scaling relationship. By scaling the self-similar object or time series, it tells us how many new pieces are revealed when it is observed at a finer resolution. Self-similarity property is represented in Figure 1.