Figure 1

The parameter region of stability and instability for ( 1.3a )-( 1.3d ) with \(\pmb{\alpha =0.8}\) . The curves \(C_{1}\), \(C_{2}\), \(C_{3}\) and \(C_{4}\) divide the plane of the parameters a, b into six regions (respectively denoted by I, II, III, IV, V and VI), where the curves \(C_{1}\) and \(C_{4}\) come from the equation \({\frac{ 4 ( a+b) ^{4}}{ ( ( a+b) ^{3}+ a-b) ^{2}}} = \tan^{2} ( \frac{2 \pi }{5} ) +1\), \(C_{2} \) from \((a+b)^{3}=0.5(b-a)\) and \(C_{3}\) from \((a+b)^{3}=b-a\). Wherein, \(d_{1}=0.02\) and \(d_{2}=0.01\).