Bifurcation and Stability in Nonlinear Dynamical Systems by Albert C. J. Luo

Author:Albert C. J. Luo
Language: eng
Format: epub
ISBN: 9783030229108
Publisher: Springer International Publishing

Table 5.1Stability and bifurcation of a 1-dimensional cubic nonlinear system in Eq. (5.61)

Fig. 5.6

a1

a2

a3

Bifurcation

(a) a0 > 0

a > max {b1, b2}

Unstable

Stable

Unstable

Second LSN

(b) a0 < 0

a > max {b1, b2}

Stable

Unstable

Stable

Second USN

(c) a0 < 0

a < min {b1, b2}

Unstable

Stable

Unstable

Second USN

(d) a0 < 0

a < min {b1, b2}

Stable

Unstable

Stable

Second LSN

Notice that , . Bifurcation condition: Δ1 = 0. LSN: lower saddle node, USN: upper saddle node

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