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Robust analytical methods are applied to find explicit expressions for the eigenvalues and eigenfunctions of the diffusion operator on a disk-shape domain with homogenous Neumann boundary conditions in polar coordinates. Spectral methods are applied using Chebyshev nonperiodic grid for the radial variable and Fourier periodic grid for the angular variable to verify the nodal lines and eigen-surfaces subject to the proposed analytical findings. The full classification of the parameter space in light of the bifurcation analysis is obtained and numerically verified by finding the solutions of the partitioning curves inducing such a classification. Spatiotemporal periodic behavior is demonstrated in the numerical solutions of the system for a proposed choice of parameters and a rigorous proof of the existence of infinitely many such points in the parameter plane is presented under a restriction on the area of the domain, with a lower bound in terms of reaction\u2013diffusion rates.<\/jats:p>","DOI":"10.1142\/s0218127418300240","type":"journal-article","created":{"date-parts":[[2018,8,8]],"date-time":"2018-08-08T09:30:23Z","timestamp":1533720623000},"page":"1830024","source":"Crossref","is-referenced-by-count":8,"title":["Domain-Dependent Stability Analysis of a Reaction\u2013Diffusion Model on Compact Circular Geometries"],"prefix":"10.1142","volume":"28","author":[{"given":"Wakil","family":"Sarfaraz","sequence":"first","affiliation":[{"name":"School of Mathematical and Physical Sciences, University of Sussex, Pevensey 3, Brighton, BN1 9QH, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anotida","family":"Madzvamuse","sequence":"additional","affiliation":[{"name":"School of Mathematical and Physical Sciences, University of Sussex, Pevensey 3, Brighton, BN1 9QH, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2018,8,8]]},"reference":[{"key":"S0218127418300240BIB001","series-title":"Monographs on Numerical Analysis","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198534679.001.0001","volume-title":"Moving Finite Elements","author":"Baines M. 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