Homoclinic Bifurcation and Chaos in a Noise-Induced <svg style="vertical-align:-0.0pt;width:25.174999px;" id="M1" height="20.9375" version="1.1" viewBox="0 0 25.174999 20.9375" width="25.174999" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.022,-0,0,-.022,.062,20.875)"><path id="x3A6" d="M488 658v-28q-47 -3 -58.5 -12t-11.5 -39q49 -2 97 -15t93.5 -39.5t73.5 -75t28 -112.5q0 -53 -19.5 -96.5t-50 -71t-70 -47t-77.5 -27.5t-75 -9q0 -36 11.5 -45.5t58.5 -12.5v-28h-223v28q47 3 58.5 12.5t11.5 45.5q-47 1 -94.5 14t-93 39.5t-74.5 76t-29 114.5
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z" /></g><g transform="matrix(.016,-0,0,-.016,16.962,10.125)"><path id="x36" d="M137 343l67 33q37 17 63 17q79 0 129.5 -53t50.5 -131q0 -92 -58 -156.5t-147 -64.5t-147 68t-58 182q0 63 17 119t43 95.5t61.5 72t69 52t67.5 31.5q62 22 128 33l6 -32q-56 -11 -108 -35q-149 -71 -184 -231zM227 337q-47 0 -95 -27q-6 -23 -6 -70q0 -93 36 -155.5
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<table>The spectral densities of bounded noise.</table>

Mathematical Problems in Engineering

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Figure 1

Figure 1: Homoclinic Bifurcation and Chaos in a Noise-Induced <svg style="vertical-align:-0.0pt;width:25.174999px;" id="M1" height="20.9375" version="1.1" viewBox="0 0 25.174999 20.9375" width="25.174999" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.022,-0,0,-.022,.062,20.875)"><path id="x3A6" d="M488 658v-28q-47 -3 -58.5 -12t-11.5 -39q49 -2 97 -15t93.5 -39.5t73.5 -75t28 -112.5q0 -53 -19.5 -96.5t-50 -71t-70 -47t-77.5 -27.5t-75 -9q0 -36 11.5 -45.5t58.5 -12.5v-28h-223v28q47 3 58.5 12.5t11.5 45.5q-47 1 -94.5 14t-93 39.5t-74.5 76t-29 114.5
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Mathematical Problems in Engineering

Homoclinic Bifurcation and Chaos in a Noise-Induced Potential

Figure 1