# Mutational Chemotaxis Motion Driven MdpI for Engineering Applications
## 4 Discussion of Experimental Results
### Parameters Sensitivity Analyses
#### 4.1.1 Determination of the Parameter \(\delta\)
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & **F1** & \multicolumn{2}{c}{**F2**} & \multicolumn{2}{c}{**F3**} \\ \cline{2-6}  & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** \\ \hline HMCMMFO\(\delta\)1 & 7.99653 \(\times 10^{3}\) & 8.11122 \(\times 10^{3}\) & 2.02180 \(\times 10^{2}\) & 7.97128 \(\times 10^{0}\) & 3.00001 \(\times 10^{2}\) & 1.60450 \(\times 10^{-3}\) \\ HMCMMFO\(\delta\)2 & 8.21015 \(\times 10^{3}\) & 8.27410 \(\times 10^{3}\) & 2.02389 \(\times 10^{2}\) & 9.48917 \(\times 10^{0}\) & 3.00002 \(\times 10^{2}\) & 5.03969 \(\times 10^{-3}\) \\ HMCMMFO\(\delta\)3 & 7.07403 \(\times 10^{3}\) & 7.66029 \(\times 10^{3}\) & 2.04935 \(\times 10^{2}\) & 1.10703 \(\times 10^{1}\) & 3.00011 \(\times 10^{2}\) & 3.91913 \(\times 10^{-2}\) \\ HMCMMFO\(\delta\)4 & 9.21663 \(\times 10^{3}\) & 8.31977 \(\times 10^{3}\) & 2.13036 \(\times 10^{2}\) & 1.76469 \(\times 10^{1}\) & 3.00009 \(\times 10^{2}\) & 1.75611 \(\times 10^{-2}\) \\ HMCMMFO\(\delta\)5 & 8.96503 \(\times 10^{3}\) & 8.71510 \(\times 10^{3}\) & 2.12881 \(\times 10^{2}\) & 4.39055 \(\times 10^{1}\) & 3.00014 \(\times 10^{2}\) & 3.99256 \(\times 10^{-2}\) \\ HMCMMFO\(\delta\)6 & 8.95832 \(\times 10^{3}\) & 8.56015 \(\times 10^{3}\) & 2.62513 \(\times 10^{2}\) & 2.31404 \(\times 10^{2}\) & 3.00007 \(\times 10^{2}\) & 1.37536 \(\times 10^{-2}\) \\ HMCMMFO\(\delta\)7 & 7.85556 \(\times 10^{3}\) & 7.53276 \(\times 10^{3}\) & 2.57079 \(\times 10^{2}\) & 1.95675 \(\times 10^{2}\) & 3.00026 \(\times 10^{2}\) & 4.89904 \(\times 10^{-2}\) \\ HMCMMFO\(\delta\)8 & 9.56777 \(\times 10^{3}\) & 8.42754 \(\times 10^{3}\) & 2.20087 \(\times 10^{2}\) & 3.05948 \(\times 10^{1}\) & 3.00038 \(\times 10^{2}\) & 8.48057 \(\times 10^{-2}\) \\ HMCMMFO\(\delta\)9 & 7.74946 \(\times 10^{3}\) & 7.93181 \(\times 10^{3}\) & 2.94503 \(\times 10^{2}\) & 4.64133 \(\times 10^{2}\) & 3.00013 \(\times 10^{2}\) & 3.65740 \(\times 10^{-2}\) \\ \hline  & **F4** & \multicolumn{2}{c}{**F5**} & \multicolumn{2}{c}{**F6**} \\ \cline{2-6}  & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** \\ \hline HMCMMFO\(\delta\)1 & 4.79600 \(\times 10^{2}\) & 2.19971 \(\times 10^{1}\) & 5.65883 \(\times 10^{2}\) & 1.30092 \(\times 10^{1}\) & 6.02914 \(\times 10^{2}\) & 1.43321 \(\times 10^{0}\) \\ HMCMMFO\(\delta\)2 & 4.83789 \(\times 10^{2}\) & 1.85106 \(\times 10^{1}\) & 5.69532 \(\times 10^{2}\) & 1.49643 \(\times 10^{1}\) & 6.04265 \(\times 10^{2}\) & 1.61646 \(\times 10^{0}\) \\ HMCMMFO\(\delta\)3 & 4.77139 \(\times 10^{2}\) & 2.38766 \(\times 10^{1}\) & 5.66750 \(\times 10^{2}\) & 1.47806 \(\times 10^{1}\) & 6.05051 \(\times 10^{2}\) & 1.54771 \(\times 10^{0}\) \\ HMCMMFO\(\delta\)4 & 4.80376 \(\times 10^{2}\) & 2.07554 \(\times 10^{1}\) & 5.65549 \(\times 10^{2}\) & 1.42534 \(\times 10^{1}\) & 6.06653 \(\times 10^{2}\) & 1.87038 \(\times 10^{0}\) \\ HMCMMFO\(\delta\)5 & 4.79813 \(\times 10^{2}\) & 1.57313 \(\times 10^{1}\) & 5.66377 \(\times 10^{2}\) & 1.65492 \(\times 10^{1}\) & 6.07038 \(\times 10^{2}\) & 3.01397 \(\times 10^{0}\) \\ HMCMMFO\(\delta\)6 & 4.76710 \(\times 10^{2}\) & 2.31167 \(\times 10^{1}\) & 5.67587 \(\times 10^{2}\) & 1.49385 \(\times 10^{1}\) & 6.08598 \(\times 10^{2}\) & 2.22007 \(\times 10^{0}\) \\ HMCMMFO\(\delta\)7 & 4.81896 \(\times 10^{2}\) & 1.71013 \(\times 10^{1}\) & 5.72513 \(\times 10^{2}\) & 2.07946 \(\times 10^{1}\) & 6.08187 \(\times 10^{2}\) & 2.06391 \(\times 10^{0}\) \\ HMCMMFO\(\delta\)8 & 4.82687 \(\times 10^{2}\) & 1.68842 \(\times 10^{1}\) & 5.70935 \(\times 10^{2}\) & 1.73829 \(\times 10^{1}\) & 6.08702 \(\times 10^{2}\) & 2.86039 \(\times 10^{0}\) \\ HMCMMFO\(\delta\)9 & 4.83429 \(\times 10^{2}\) & 1.40439 \(\times 10^{1}\) & 5.74763 \(\times 10^{2}\) & 1.63916 \(\times 10^{1}\) & 6.09976 \(\times 10^{2}\) & 2.59386 \(\times 10^{0}\) \\ \hline  & **F7** & \multicolumn{2}{c}{**F8**} & \multicolumn{2}{c}{**F9**} \\ \cline{2-6}  & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** \\ \hline HMCMMFO\(\delta\)1 & 8.08829 \(\times 10^{2}\) & 1.93631 \(\times 10^{1}\) & 8.66175 \(\times 10^{2}\) & 1.65266 \(\times 10^{1}\) & 1.02209 \(\times 10^{3}\) & 1.18813 \(\times 10^{2}\) \\ HMCMMFO\(\delta\)2 & 8.11975 \(\times 10^{2}\) & 1.93645 \(\times 10^{1}\) & 8.61202 \(\times 10^{2}\) & 1.37233 \(\times 10^{1}\) & 1.05695 \(\times 10^{3}\) & 1.124  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{2}{c}{**F13**} & \multicolumn{2}{c}{**F14**} & \multicolumn{2}{c}{**F15**} \\ \cline{2-7}  & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** \\ \hline HMCMMFO\(\delta 1\) & \(3.33690\times 10^{4}\) & \(2.50935\times 10^{4}\) & \(2.81393\times 10^{4}\) & \(1.49900\times 10^{4}\) & \(2.01635\times 10^{4}\) & \(1.44834\times 10^{4}\) \\ HMCMMFO\(\delta 2\) & \(2.89474\times 10^{4}\) & \(2.19148\times 10^{4}\) & \(2.25083\times 10^{4}\) & \(1.19023\times 10^{4}\) & \(1.17364\times 10^{4}\) & \(1.22589\times 10^{4}\) \\ HMCMMFO\(\delta 3\) & \(3.91207\times 10^{4}\) & \(2.61488\times 10^{4}\) & \(2.98529\times 10^{4}\) & \(1.43223\times 10^{4}\) & \(1.38299\times 10^{4}\) & \(1.34655\times 10^{4}\) \\ HMCMMFO\(\delta 4\) & \(4.52750\times 10^{4}\) & \(2.44167\times 10^{4}\) & \(2.96832\times 10^{4}\) & \(1.51745\times 10^{4}\) & \(1.87379\times 10^{4}\) & \(1.49142\times 10^{4}\) \\ HMCMMFO\(\delta 5\) & \(3.47647\times 10^{4}\) & \(2.61895\times 10^{4}\) & \(2.11498\times 10^{4}\) & \(8.92111\times 10^{3}\) & \(8.07613\times 10^{3}\) & \(9.03779\times 10^{3}\) \\ HMCMMFO\(\delta 6\) & \(3.59667\times 10^{4}\) & \(2.59839\times 10^{4}\) & \(2.73962\times 10^{4}\) & \(1.45910\times 10^{4}\) & \(1.15598\times 10^{4}\) & \(1.34873\times 10^{4}\) \\ HMCMMFO\(\delta 7\) & \(3.56409\times 10^{4}\) & \(2.61362\times 10^{4}\) & \(3.32410\times 10^{4}\) & \(1.96918\times 10^{4}\) & \(8.27325\times 10^{3}\) & \(9.80176\times 10^{3}\) \\ HMCMMFO\(\delta 8\) & \(4.00782\times 10^{4}\) & \(2.83890\times 10^{4}\) & \(2.78522\times 10^{4}\) & \(1.47880\times 10^{4}\) & \(9.22414\times 10^{3}\) & \(1.02606\times 10^{4}\) \\ HMCMMFO\(\delta 9\) & \(3.70569\times 10^{4}\) & \(3.41490\times 10^{4}\) & \(3.25110\times 10^{4}\) & \(1.91208\times 10^{4}\) & \(8.78055\times 10^{3}\) & \(9.08876\times 10^{3}\) \\ \hline  & \multicolumn{2}{c}{**F16**} & \multicolumn{2}{c}{**F17**} & \multicolumn{2}{c}{**F18**} \\ \cline{2-7}  & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** \\ \hline HMCMMFO\(\delta 1\) & \(2.26587\times 10^{3}\) & \(2.54360\times 10^{2}\) & \(2.03413\times 10^{3}\) & \(1.66456\times 10^{2}\) & \(2.32120\times 10^{5}\) & \(1.62629\times 10^{5}\) \\ HMCMMFO\(\delta 2\) & \(2.22922\times 10^{3}\) & \(2.62825\times 10^{2}\) & \(1.98976\times 10^{3}\) & \(1.45363\times 10^{2}\) & \(3.03816\times 10^{5}\) & \(2.64694\times 10^{5}\) \\ HMCMMFO\(\delta 3\) & \(2.18807\times 10^{3}\) & \(2.03828\times 10^{2}\) & \(1.96657\times 10^{3}\) & \(1.63256\times 10^{2}\) & \(3.02479\times 10^{5}\) & \(2.53518\times 10^{5}\) \\ HMCMMFO\(\delta 4\) & \(2.27606\times 10^{3}\) & \(3.00368\times 10^{2}\) & \(1.93906\times 10^{3}\) & \(1.38437\times 10^{2}\) & \(2.18571\times 10^{5}\) & \(1.592221\times 10^{5}\) \\ HMCMMFO\(\delta 5\) & \(2.25724\times 10^{3}\) & \(3.05542\times 10^{2}\) & \(1.93626\times 10^{5}\) & \(1.30135\times 10^{2}\) & \(2.11116\times 10^{5}\) & \(1.23450\times 10^{5}\) \\ HMCMMFO\(\delta 6\) & \(2.19430\times 10^{3}\) & \(2.51897\times 10^{2}\) & \(1.94892\times 10^{3}\) & \(1.71728\times 10^{2}\) & \(2.38839\times 10^{5}\) & \(1.14788\times 10^{5}\) \\ HMCMMFO\(\delta 7\) & \(2.17115\times 10^{3}\) & \(2.78175\times 10^{2}\) & \(1.96743\times 10^{3}\) & \(1.61969\times 10^{2}\) & \(2.21677\times 10^{5}\) & \(2.13197\times 10^{5}\) \\ HMCMMFO\(\delta 8\) & \(2.18195\times 10^{3}\) & \(2.54818\times 10^{2}\) & \(1.97014\times 10^{3}\) & \(1.45771\times 10^{2}\) & \(2.68645\times 10^{5}\) & \(2.06891\times 10^{5}\) \\ HMCMMFO\(\delta 9\) & \(2.25173\times 10^{3}\) & \(3.14991\times 10^{2}\) & \(1.94118\times 10^{3}\) & \(1.46154\times 10^{2}\) & \(2.30345\times 10^{5}\) & \(1.04406\times 10^{5}\) \\ \hline  & \multicolumn{2}{c}{**F19**} & \multicolumn{2}{c}{**F20**} & \multicolumn{2}{c}{**F21**} \\ \cline{2-7}  & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** \\ \hline HMCMMFO\(\delta 1\) & \(2.45014\times 10^{4}\) & \(2.20795\times 10^{4}\) & \(2.36142\times 10^{3}\) & \(2.13054\times 10^{2}\) & \(2.37248\times 10^{3}\) & \(1.64518\times 10^{1}\) \\ HMCMMFO\(\delta 2\) & \(2.71886\times 10^{4}\) & \(2.44299\times 10^{4}\) & \(2.29151\times 10^{3}\) & \(1.78105\times 10^{2}\) & \(2.36374\times 10^{3}\) & \(1.33238\times 10^{1}\) \\ HMCMMFO\(\delta 3\) & \(2.38428\times 10^{4}\) & \(2.00474\times 10^{4}\) & \(2.31589\times 10^{3}\) & \(1.44362\times 10^{2}\) & \(2.35438\times 10^{3}\) & \(1.37493\times 10^{1}\) \\ HMCMMFO\