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Ferroelectric frontiers: Navigating phase portraits, chaos, multistability and sensitivity in thin-film dynamics

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  • Jhangeer, Adil
  • Beenish,

Abstract

This research includes the study of the non-linear dynamics of thin-film ferroelectric materials governed by an equation of wave dynamics within the material. This equation plays a key role in both physics and the study of aqueous flow. The work is planned as examining the symmetries group analysis drops, studying the dynamical system features through bifurcation phase portraits, and carrying dynamic phenomena in chaos theory. Diverse techniques are taken, such as Lyapunov exponent, 2D, and 3D phase portraits, Poincaré maps, time series analysis, and sensitivity to multistability under the different conditions of the initial state. In addition, the study involves using the extended hyperbolic function method to obtain the general analytical solutions via which various kinds of solitary wave solutions are produced including trigonometric and hyperbolic functions and periodic, bright, and singular soliton solutions. These solutions are followed by a list of constraint conditions in the form of equations. Visual data of 2D, 3D, and contour plots are presented, with parameters carefully set to reflect various scenarios. Sensitivity analysis is performed using alternative initial conditions, and stability analysis is demonstrated graphically. To fully grasp the dynamic features of these systems and accurately predict outcomes, it is essential to advance new technologies and methodologies that can further enhance our understanding and predictive capabilities in complex systems.

Suggested Citation

  • Jhangeer, Adil & Beenish,, 2024. "Ferroelectric frontiers: Navigating phase portraits, chaos, multistability and sensitivity in thin-film dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:chsofr:v:188:y:2024:i:c:s0960077924010920
    DOI: 10.1016/j.chaos.2024.115540
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    References listed on IDEAS

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    1. A. K. Bandyopadhyay & P. C. Ray & V. Gopalan, 2008. "Solitons and critical breakup fields in lithium niobate type uniaxial ferroelectrics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 65(4), pages 525-531, October.
    2. Ma, Wen-Xiu, 2024. "Binary Darboux transformation of vector nonlocal reverse-time integrable NLS equations," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    3. Faridi, Waqas Ali & Wazwaz, Abdul-Majid & Mostafa, Almetwally M. & Myrzakulov, Ratbay & Umurzakhova, Zhanar, 2024. "The Lie point symmetry criteria and formation of exact analytical solutions for Kairat-II equation: Paul-Painlevé approach," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    4. Jhangeer, Adil & Beenish,, 2024. "Study of magnetic fields using dynamical patterns and sensitivity analysis," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    5. Houwe, Alphonse & Abbagari, Souleymanou & Akinyemi, Lanre & Doka, Serge Yamigno & Metwally, Ahmed Sayed M. & Ahmad, Hijaz, 2024. "Bifurcation and chaotic patterns of the solitary waves in nonlinear electrical transmission line lattice," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    6. Liya Yang & Houbing Huang & Zengzhe Xi & Limei Zheng & Shiqi Xu & Gang Tian & Yuzhi Zhai & Feifei Guo & Lingping Kong & Yonggang Wang & Weiming Lü & Long Yuan & Minglei Zhao & Haiwu Zheng & Gang Liu, 2022. "Simultaneously achieving giant piezoelectricity and record coercive field enhancement in relaxor-based ferroelectric crystals," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
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