Table 3 Regression results of the Haken model.

From: Research on the synergistic effects of urbanization and ecological environment in the Chengdu–Chongqing urban agglomeration based on the Haken model

Serial number

Model assumptions

Equations of motion

Control variables

Conclusion

①

q1 = UR

q2 = EG

q1(t) = 1.1095***q1(t − 1) − 0.0791***q1(t − 1)q2(t − 1) q2(t) = 0.9669***q2(t − 1) − 0.0470***q12(t − 1)

γ1 = −1095, a = 0.0791, γ2 = 0.0331, b = − 0.0470

(1) The equations of motion hold true

(2) The adiabatic approximation assumption is satisfied

(3) The model assumptions are valid, with urbanization as the serial parameter

②

q1 = EG

q2 = UR

q1(t) = 1.0510***q1(t − 1) − 0.0900***q1(t − 1)q2(t − 1)

q2(t) = 1.0259***q2(t − 1) + 0.0466***q12(t − 1)

γ1 = − 0.0510, a = 0.0900, γ2 = − 0.0259, b = 0.0466

(1) The equations of motion are valid

(2) The adiabatic approximation assumption is not met

(3) The model assumptions are not valid

  1. *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively. No “*” indicates insignificance.
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