Saddle-node bifurcation parameter detection strategy with nested-layer particle swarm optimization.

Highlights • NLPSO is a non-Lyapunov bifurcation parameter detection strategy. • Problems in detecting saddle-node bifurcation parameters by NLPSO were clarified. • The problems were solved by imposing a simple condition on the objective function. • The extended NLPSO accurately detected saddle-node bifurcation parameters. Abstract Nested-layer particle swarm optimization (NLPSO) detects bifurcation parameters in discrete-time dynamical systems. Previous studies have proven the effectiveness of NLPSO for period-doubling bifurcations, but not for other bifurcation phenomena. This paper demonstrates that NLPSO can effectively detect saddle-node bifurcations. Problems in detecting saddle-node bifurcation parameters by conventional NLPSO are clarified, and are solved by imposing a simple condition on the NLPSO objective function. Under this conditional objective function, the NLPSO accurately detected both saddle-node and period-doubling bifurcation parameters regardless of their stability, without requiring careful initialization, exact calculations or Lyapunov exponents. [ABSTRACT FROM AUTHOR]