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Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 1 The impact of k on the values of \(\omega _{0}^{*}\) and \(\tau _{0}^{*}\) for the controlled system (5.2) with \(q_{1}=0.91\), \(q_{2}=0.98\), \(q_{3}=0.95\)

From: On the reasonability of linearized approximation and Hopf bifurcation control for a fractional-order delay Bhalekar–Gejji chaotic system

Feedback gain k

Critical frequency \(\omega _{0}^{*}\)

Bifurcation point \(\tau _{0}^{*}\)

−3

9.653358584

0.108321963

−2.5

9.595547511

0.106433652

−2

9.539410105

0.104408781

−1.5

9.485911614

0.102254645

−1

9.436041308

0.099984585

−0.5

9.390741645

0.097617839

0

9.350834520

0.095178561

0.5

9.316958928

0.092694075

1

9.289532626

0.090192707

1.5

9.268743775

0.087701612

2

9.254570242

0.085245013

2.5

9.246818131

0.082843069

3

9.245168793

0.080511419

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