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Chaotic dynamics and Lyapunov analysis of the Benney–Luke equation for image encryption

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  • Samina, Samina
  • Wali, Samad

Abstract

Shallow water wave models play a crucial role in understanding nonlinear wave interactions and have wide-ranging applications in fluid dynamics. Among them, the Benney–Luke equation stands out as a key model for describing two-way water wave propagation. However, a detailed study connecting its soliton behavior with chaotic dynamics and real-world applications has been limited. In this work, we use the Kudryashov method to obtain new analytical soliton solutions covering singular, dark, and bright types for the Benney–Luke equation. By applying a Galilean transformation, the equation is further expressed as a dynamical system, whose bifurcations, multistability, and chaotic behavior are explored through phase portraits, Lyapunov exponents, and sensitivity analyses. Our results show that the system displays diverse dynamics, including the coexistence of chaotic and periodic attractors (multistability) that depend on initial conditions. Leveraging this complexity, we implement the chaotic system as a pseudo-random number generator within a secure image encryption framework. The scheme achieves high security, with near-ideal entropy (7.9998) and strong sensitivity (NPCR>99.6%).

Suggested Citation

  • Samina, Samina & Wali, Samad, 2026. "Chaotic dynamics and Lyapunov analysis of the Benney–Luke equation for image encryption," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 683(C).
    • Handle: RePEc:eee:phsmap:v:683:y:2026:i:c:s0378437125008507
    DOI: 10.1016/j.physa.2025.131198
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    References listed on IDEAS

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