Fig 1.
Illustrates fc versus b under different δ values.
Vertically, with increasing δ, the system evolves to a stable state with a greater degree of cooperation. Showing that the proposed mechanism promotes cooperation and broadens its disappearance threshold b. Parameters are set to β = 2, α = 0.5 based on Ref. [24] and L = 200.
Fig 2.
Illustrates temporal evolution of cooperative for some δ values, showing that the proposed mechanism can promote cooperation.
With increasing δ, the system evolves to a stable state with a greater degree of cooperation. The results indicate that higher parameter δ can promote cooperation. Parameters are set to β = 2, α = 0.5 and L = 200.
Fig 3.
Shows snapshots of spatial distributions for blue cooperators and purple defectors at different MCS for various δ value.
Vertically, the diffusion of cooperative behavior accelerates with increasing δ. Simulations indicate that larger δ significantly promotes cooperation. Parameters are set to b = 1.1, α = 0.5, β = 2 and L = 200.
Fig 4.
Panel (a) plots the fc against the b for different β values.
Panel (b) demonstrates the dynamic impact of the β on cooperation evolution, revealing that while higher β values promote cooperation, the effect is only significant up to a certain threshold. The results indicate that a modestly sensitivity parameter β can promote cooperation. Parameters are set to α = 0.5, δ = 1.0 and L = 200.
Fig 5.
Panel (a) plots the fc against the b under different α values, Panel (b) shows the dynamic impact of α on the cooperative evolution, demonstrating that high consistency aspiration or goal suppress the propagation of cooperative behavior in the system.
The results indicate that lower system consistency desires or goals can promote cooperation. Parameters are set to β = 2, δ = 1.0 and L = 200.
Fig 6.
Illustrates the dynamic evolution of fc with parameter β-α.
Horizontally, system cooperation increases as β increases, whereas vertically, it decreases as α increases. The results indicate that parameters β and δ jointly determine the cooperative evolution in the system. Parameters are set to δ = 1.0 and L = 200.
Fig 7.
Panel (a) plots the fc against the b under different K values.
Panel (b) plots the fc against the b under different L values. The result is consistent. The system exhibits robustness against minor noise interference and differences in network scale. Which indicating that the system is robust. Parameters are set to β = 2, α = 0.5, δ = 0.2 and L = 200 in Panel (a), and β = 2, α = 0.5, δ = 0.2 and K = 0.5 in Panel (b).