Browsing by Author "Dr. Muhammad Yousaf, Assistant Profesor"

Filter results by typing the first few letters
Now showing 1 - 2 of 2
  • No Thumbnail Available
    Item
    Two Population Neural Field Model With Constant External Input
    (Library Information Services, COMSATS University, Lahore Campus, 2018) Ammara Basharat,; FA16-RMT-032; Dr. Muhammad Yousaf, Assistant Profesor; LHR TP 5195
    In this work, We have study the two-population neural field Model under the effect of constant external inputs. Earlier, Blomquist et al.[1] investigated the stationary symmetric solution of two population model with no external input.They found that Amari stability analysis and linearized stability analysis produces same results. Later on Yousaf et al. [2] investigated the same model under the influence of spatial dependent external input and proved that the Amari technique and linearized stability technique does not produce same results. They also investigate the number of bumps as a function of amplitude parameter of external input and found at most four bump pairs. In our research work, We have to explore the two population neural field model under the effect of constant external input on bump solutions. We further, have to investigate the stability properties of stationary symmetric solutions by using two approaches (i) Amari approach (ii) standard linearized approach. Numerically, We will investigate the number of bumps as a function of width and amplitude parameter of external input
  • No Thumbnail Available
    Item
    Two Population Neural Field Model With Gaussian External Input
    (Library Information Services, COMSATS University, Lahore Campus, 2019) Sana Javed; , FA17-RMT-006; Dr. Muhammad Yousaf, Assistant Profesor; LHR TP 56440
    n this, we have explored Gaussian spatio-temporal external input on per sistent activity states. The aim of work was to build up a numerical scheme of action for two population model with Gaussian external input. We breakup the external input into 3 parts i.e., amplitude, the spatial part and the tem poral part . In temporal part, we use Gaussian type external input. We have explored the boundedness, uniqueness for the present choice of work. We check the emergence then we examine the stationary solution called ”bumps”. This model is the continuation of Patrick et al [37] by extending the spatio-temporal Gaussian type external input. We have check thoroughly the broad bump so lution. We also check the activity will converge, when the broad bump is less than cr. The present choice of H(x,t) produce better result as compare to Yousaf et al