Department of Mathematics

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Author: search.filters.author.Dr. Muhammad Yousaf BhattiSubject: search.filters.subject.Bump Solutions

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    Emergence of Bumps for Piece Wise Defined External Input in a Two-Population Neural Field Model
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) ATTIQA CHAUDHARY; CIIT/FA19-RMT-016/LHR; Dr. Muhammad Yousaf Bhatti; LHR TP 7391
    In this research, we have studied the appearance of bump solutions (localized activity states) in a two-population neural field model for the temporary external input that depends on space and time with piece wise define temporal part. The same model has been investigated by Blomquist et al [2] with no external input and later on by Yousaf et al with spatial and spatio temporal dependent external inputs [3,5]. Zeshan et al [4] investigated the same model for more realistic approach for temporal function (𝛼-type function) in the spatio external input. In present study, we explored the appearance of bump solutions (persistent localized activity states) for more detailed temporal part (piece wise defined) in the spatio external input of for the above said model. The effect of external input on appearance of bumps for different spatial, piece wise 𝛼-type temporal functions of external input is investigated and found that certain parameters play a key role in the generation of persistent activity states in the network e.g. 𝜏(relative inhibition time constant), 𝑇𝑒 (total duration), 𝐶𝑒(amplitude), 𝑡1(inclination peak time) and 𝑡2 (Peak time duration) of external input. It is found that the minimum values of the amplitude and active time to evoke the activity in the network is smaller than those observed in prior studies. These results show that the present choice of temporal functions in the external input is more effective and efficient
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    Annihilation of Bumps for Piecewise Defined External Input in a Two-Population Neural field Model
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Ayesha Laraib; CIIT/FA19-RMT-010/LHR; Dr. Muhammad Yousaf Bhatti; LHR TP 7392
    In this Research Proposal, we have to analyze the Annihilation mechanism of persistent localized activity states (bumps) in response to transient Spatio-temporal external input with piecewise temporal function in two-population neural field model of the Wilson-Cowan type [1]. Blomquist et al.[2] explored the bump solutions of two- population neural field models with no external input. Two separate methodologies are utilized to investigate the stability of bumps, the Amari methodology and direct linearization process stability. It was shown both mathematically and numerically that Ammari and full linearized stability produces same results. Directly after, the same model was investigated by spatial dependent and Spatio- temporal external input, by Yousaf .et. al [3, 4]. Afzal. Z [5, 6] studied the bump solution of a two-population neural field model with a smooth $alpha$-type temporal function under the effect of transitory Spatio-temporal external input. For a detailed exploration of the effects of different parameters of external input, it was further classified into amplitude, spatial, and temporal parts. We are investigating the annihilation of localized activity states (bumps) in response to transient Spatio- temporal external input with piecewise temporal function in a two-population neural field model of the Wilson-Cowan type. In the 4th chapter, we will present the conclusion of our thesis. In the 5th chapter, we will present the references of our thesis.