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Table 4 Local stability analysis results in each scenario

From: Evolutionary game model of health care and social care collaborative services for the elderly population in China

Equilibrium point

Scenario 1

Scenario 2

Scenario 3

Scenario 4

\(det J\)

\(tr J\)

Result

\(det J\)

\(tr J\)

Result

\(det J\)

\(tr J\)

Result

\(det J\)

\(tr J\)

Result

\(O\left(0, 0\right)\)

\(+\)

\(-\)

ESS

\(-\)

\(\pm\)

Saddle

\(-\)

\(\pm\)

Saddle

\(+\)

\(+\)

Unstable

\(A\left(0, 1\right)\)

\(+\)

\(+\)

Unstable

\(-\)

\(\pm\)

Saddle

\(+\)

\(+\)

Unstable

\(-\)

\(\pm\)

Saddle

\(B\left(1, 0\right)\)

\(+\)

\(+\)

Unstable

\(+\)

\(+\)

Unstable

\(-\)

\(\pm\)

Saddle

\(-\)

\(\pm\)

Saddle

\(C \left(1, 1\right)\)

\(+\)

\(-\)

ESS

\(+\)

\(-\)

ESS

\(+\)

\(-\)

ESS

\(+\)

\(-\)

ESS

\(E\left({x}^{*}, {y}^{*}\right)\)

\(-\)

0

Saddle

  

None

  

None

  

None