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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