Adaptive-Impulsive Control of the Projective Synchronization in Drive-Response Complex Dynamical Networks with Time-Varying Coupling

<table>PS errors under the adaptive-impulsive control: (a) <svg height="16.4125" id="M109" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 126.375 16.4125" width="126.375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.017,-0,0,-.017,16.688,12.138)"><path d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" id="x28"></path></g><g transform="matrix(.017,-0,0,-.017,22.569,12.138)"><path d="M324 430l-26 -36l-112 -4l-55 -265q-13 -66 7 -66q13 0 44.5 20t50.5 40l17 -24q-38 -40 -85.5 -73.5t-87.5 -33.5q-50 0 -21 138l55 262h-80l-2 8l25 34h66l25 99l78 63l10 -9l-37 -153h128z" id="x1D461"></path></g><g transform="matrix(.017,-0,0,-.017,28.366,12.138)"><path d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" id="x29"></path></g><g transform="matrix(.017,-0,0,-.017,38.956,12.138)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,53.66,12.138)"><use xlink:href="#x1D465"></use></g>
<g transform="matrix(.012,-0,0,-.012,63.162,16.212)"><use xlink:href="#x1D456"></use></g><g transform="matrix(.012,-0,0,-.012,66.411,16.212)"><use xlink:href="#x31"></use></g>
<g transform="matrix(.017,-0,0,-.017,76.525,12.138)"><path d="M535 230h-483v50h483v-50z" id="x2212"></path></g><g transform="matrix(.017,-0,0,-.017,90.277,12.138)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
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<g transform="matrix(.012,-0,0,-.012,119.975,16.212)"><use xlink:href="#x31"></use></g>
</svg>, (b) <svg height="16.4125" id="M110" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 126.375 16.4125" width="126.375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.138)"><use xlink:href="#x1D452"></use></g>
<g transform="matrix(.012,-0,0,-.012,7.1,16.212)"><use xlink:href="#x1D456"></use></g><g transform="matrix(.012,-0,0,-.012,10.348,16.212)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
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Mathematical Problems in Engineering

fig2

Figure 2

Figure 2: Adaptive-Impulsive Control of the Projective Synchronization in Drive-Response Complex Dynamical Networks with Time-Varying Coupling 