Nonlinear Dynamics and Bifurcation Structure of a Stage-Structured Theta-Ricker Map with Cross-Stage Feedback

This study surveyed the nonlinear dynamics of a discrete-time, stage-structured population model merging demographic memory through adult survival. The model develops the classical θ–Ricker formulation by introducing cross-stage feedback between juvenile and adult compartments governed by a set of biologically interpretable parameters. The analytical results show that the system admits a unique positive equilibrium, the local stability of which is determined by the trace and determinant of the Jacobian matrix. Loss of stability occurs via two primary mechanisms: flip (period doubling) and Neimark–Sacker bifurcations. Explicit conditions for both bifurcations are derived, and the first Lyapunov coefficient is computed to characterize the direction and criticality of the Neimark–Sacker (NS) transition. Numerical experiments, including one-parameter bifurcation diagrams and two-parameter Lyapunov maps, confirmed the analytical predictions. Increasing the reproductive rate or cross-stage feedback leads to successive period doubling and chaos, whereas higher maturation efficiency and adult survival expand the stability domain. The results revealed that demographic memory acts as an internal damping mechanism that delays the onset of instability and suppresses chaotic oscillations. Overall, this study provides a coherent analytical–numerical framework for understanding how feedback and memory interact to shape complex population dynamics in stage-structured ecological systems.