  Dynamic environments shape diverse dynamics in evolutionary game systems. We
introduce spatial heterogeneity of resources into the Prisoner's Dilemma Game
model to explore the co-evolution of individuals' strategies and environmental
resources. The adequacy of resources significantly affects the survival
competitiveness of surrounding individuals. Feedback between individuals'
strategies and the resources they can use leads to the dynamic of the
"oscillatory tragedy of the commons". Our findings indicate that when the
influence of individuals' strategies on the update rate of resources is
significantly high, individuals can form sustained spatial clustered patterns.
These sustained patterns can directly trigger a transition in the system from
the persistent periodic oscillating state to an equilibrium state. These
findings align with observed phenomena in real ecosystems, where organisms
organize their spatial structures to maintain system stability. We discuss
critical phenomena in detail, demonstrating that the aforementioned phase
transition is robust across various system parameters including: the strength
of cooperators in restoring the environment, the initial distributions of
cooperators, and noise.
