Calculations of Lyapunov exponents and characterizations of nonlinear dynamics in bulk antiferroelectrics

Abstract

This paper investigates the influence of the amplitude, frequency, and damping of the applied field on the maximal Lyapunov exponents and chaotic dynamics in the bulk antiferroelectric (AFE) system. Numerical simulations are conducted in three parts. First, Wolf’s algorithm calculates the Lyapunov exponents with varying frequencies and a constant amplitude. The second part varies the amplitude while keeping the frequency constant. Two sets of data are generated for small (g = 0.01) and large (g = 0.3) damping values. In the third part, selected parameters produce phase portraits based on the positive and negative Lyapunov exponents using the fourth-order Runge–Kutta method. The results show that the Lyapunov exponent identifies chaotic and periodic regimes with small damping, but this becomes less evident with large damping. The study also demonstrates that manipulating the applied field parameters enables control over chaotic and periodic responses in the bulk AFE system.

Keywords

• Lyapunov exponents
• antiferroelectrics
• ammonium dihydrogen phosphate
• chaos
• nonlinear
• periodic response