Exploring chaos and stability: dynamic insights into the stochastic Davey-Stewartson system through advanced sensitivity analysis

Abstract

In this study, we investigate the stochastic Davey-Stewartson equation in the presence of noise. These two-dimensional integrable equations are higher-dimensional versions of the nonlinear Schrödinger equation. Davey-Stewartson equations are important in plasma physics, nonlinear optics, hydrodynamics, and other disciplines because the solutions they provide are valuable in understanding many complex physical phenomena. We employ a modified version of the $$\left( \frac{G'}{G^2} \right)$$ G ′ G 2 approach to handle variable-coefficient systems with imaginary components, such as nonlinear Schrödinger systems. We have discovered a wide range of precise traveling wave solutions, including solitons, kink, periodic, and rational solutions. These solutions may have a significant impact in the domains of engineering and plasma physics. The presented techniques effectively achieve a variety of exponential solutions, including bright, dark, single, rational, and periodic solitary wave solutions. We used MATLAB to simulate our findings and provide 3D, 2D, and counter graphs that illustrate the impact of noise on the precise solutions of the stochastic Davey-Stewartson problem. We apply the Galilean transformation to derive the planar dynamical system, which enhances our understanding of the system’s dynamical analysis. We also conduct a sensitivity analysis to observe the systematic response to various initial conditions. This analysis focuses on the symmetrical aspects of the system and includes the illustration of phase portraits with equilibrium points. We also investigate the chaotic behavior of the planer dynamical system by introducing an additional external force. We predict the system’s behavior to increase the value of intensity and frequency. Our analysis reveals periodic, quasi-periodic, and chaotic processes.

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