Multistability and Instability of Competitive Neural Networks with Mexican-Hat-Type Activation Functions

<table>Phase plot of state variable <svg height="20.4125" id="M563" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 80.025002 20.4125" width="80.025002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,59.2,20.35)"><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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<g transform="matrix(.012,-0,0,-.012,71.413,8.1)"><path d="M649 676l-22 -187l-33 -2q3 56 -12 94q-8 20 -31.5 26.5t-86.5 6.5h-74l-90 -491q-4 -23 -6 -36.5t1 -25t7 -16.5t18 -9t27 -5t41 -3l-6 -28h-286l4 28q68 5 84 18.5t28 76.5l94 491h-55q-74 0 -100.5 -6t-41.5 -23q-24 -29 -54 -98l-32 1q32 98 53 188h22q7 -18 15 -22
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</svg> in Example <a href="https://static.hindawi.com/articles/aaa/volume-2014/901519/figures/#ex2">2</a>.</table>

Abstract and Applied Analysis

fig16

Figure 16

Figure 16: Multistability and Instability of Competitive Neural Networks with Mexican-Hat-Type Activation Functions 