Dynamics of a New Hyperchaotic System with Only One Equilibrium Point

<table>Period-doubling bifurcation in <svg height="11.825" id="M83" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 49.325001 11.825" width="49.325001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M536 404q0 -17 -13.5 -31.5t-26.5 -14.5q-8 0 -15 10q-11 14 -25 14q-22 0 -67 -50q-47 -52 -68 -82l37 -102q31 -88 55 -88t78 59l16 -23q-32 -48 -68.5 -78t-65.5 -30q-19 0 -37.5 20t-29.5 53l-41 116q-72 -106 -114.5 -147.5t-79.5 -41.5q-21 0 -34.5 14t-13.5 37
q0 16 13.5 31.5t28.5 15.5q12 0 17 -11q5 -10 25 -10q22 0 57.5 36t89.5 111l-40 108q-22 58 -36 58q-21 0 -67 -57l-19 20q81 107 125 107q17 0 30 -22t39 -88l22 -55q68 92 108.5 128.5t74.5 36.5q20 0 32.5 -14t12.5 -30z" id="x1D465"></path></g>
<g transform="matrix(.012,-0,0,-.012,9.563,11.762)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
<g transform="matrix(.017,-0,0,-.017,19.675,7.675)"><path d="M535 230h-483v50h483v-50z" id="x2212"></path></g><g transform="matrix(.017,-0,0,-.017,33.427,7.675)"><path d="M536 404q0 -17 -13.5 -31.5t-26.5 -14.5q-8 0 -15 10q-11 14 -25 14q-22 0 -67 -50q-47 -52 -68 -82l37 -102q31 -88 55 -88t78 59l16 -23q-32 -48 -68.5 -78t-65.5 -30q-19 0 -37.5 20t-29.5 53l-41 116q-72 -106 -114.5 -147.5t-79.5 -41.5q-21 0 -34.5 14t-13.5 37
q0 16 13.5 31.5t28.5 15.5q12 0 17 -11q5 -10 25 -10q22 0 57.5 36t89.5 111l-40 108q-22 58 -36 58q-21 0 -67 -57l-19 20q81 107 125 107q17 0 30 -22t39 -88l22 -55q68 92 108.5 128.5t74.5 36.5q20 0 32.5 -14t12.5 -30z" id="x1D465"></path></g>
<g transform="matrix(.012,-0,0,-.012,42.938,11.762)"><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>
</svg> plane <svg height="15.0875" id="M84" style="vertical-align:-2.3205pt" version="1.1" viewbox="0 0 60.650002 15.0875" width="60.650002" 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)"><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,-.017,5.944,12.138)"><path d="M515 96q-37 -44 -84.5 -76t-71.5 -32q-12 0 -18 7t-6 34t10 75l19 89h-2q-87 -113 -181 -176q-43 -29 -83 -29q-46 0 -46 63q0 31 9 67l52 222q7 36 -1 36q-10 0 -76 -50l-13 24q47 45 92 71.5t67 26.5q18 0 21 -16.5t-8 -65.5l-56 -242q-16 -67 13 -67q41 0 114 74
t114 146l32 145l74 26h11q-52 -199 -80 -347q-8 -39 6 -39q7 0 32 17.5t47 39.5z" id="x1D462"></path></g><g transform="matrix(.017,-0,0,-.017,19.798,12.138)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,34.502,12.138)"><path d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5
q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z" id="x33"></path></g><g transform="matrix(.017,-0,0,-.017,42.661,12.138)"><path d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z" id="x2E"></path></g><g transform="matrix(.017,-0,0,-.017,46.537,12.138)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g><g transform="matrix(.017,-0,0,-.017,54.696,12.138)"><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>
</svg>.</table>

Journal of Mathematics

fig9

Figure 9

Figure 9: Dynamics of a New Hyperchaotic System with Only One Equilibrium Point 