Stability and hopf bifurcation analysis for a class of heterogeneous-order liouville-caputo fractional differential systems

Abstract This study innovatively constructs and analyzes a predator-prey system featuring heterogeneous memory effects. The model employs distinct Liouville-Caputo fractional derivatives for prey and predator dynamics and integrates both cannibalism and predator-induced fear effects, thereby overcoming the limitations of uniform-order systems. A progressive analysis was conducted: for identical orders, solution uniqueness and boundedness were verified, and conditions for positive equilibrium, stability, and Hopf bifurcation were derived; for distinct orders, stability and bifurcation conditions were obtained via parametric curves relating the characteristic equation to the fractional-order parameters. Numerical experiments confirmed that cannibalism, the fear effect, and fractional orders independently and synergistically regulate equilibrium stability, triggering Hopf bifurcation and population oscillations. These results highlight the synergistic role of behavioral mechanisms and memory heterogeneity in ecological dynamics.