Coexistence of Boundary Limit Cycles and Interior Limit Cycles in the 4D Lotka–Volterra Competitive System

We investigate the distribution and number of limit cycles in a Four-Dimensional Lotka–Volterra (4DLV) competitive system. By combining the second focus value and the theory of carrying simplex, we rigorously prove the coexistence of boundary limit cycles and interior limit cycles. Notably, the 4DLV competitive system can admit at least five limit cycles whose determinants of linearized matrices at their respective critical parameters have different signs.