Scholarlink

<p>The dynamics of the Slobodan–Zdravković (SZ) model was extended by simultaneously taking into account the fractional order <i>e</i> and the long-range interactions (LRI) of each dimer. We show that, the dynamics of the model is reduced to a nonlinear fractional Schrödinger equation, where the coefficients of dispersion and the nonlinearity depend strongly on the fractional derivative order parameter <i>e</i> and LRI coefficient <i>s</i>. We found that, for low values of <i>s</i>, the microtubules self-assemble and exhibit an unusual behaviour, undergoing alternating periods of growth and shrinkage (catastrophe), with rapid transitions between these states. The high values of <i>s</i> lead to the inverse process, known as rescue. Finally, one obtained the transition for high values of <i>s</i>. At this stage of high values of <i>s</i>, the wave amplitude decreases with time, showing that the system loses energy; therefore, the necessary information for the construction of proteins is lost. It turns out that the LRI is a valuable tool for monitoring the evolution of a biomolecular system, particularly when certain parameters change, such as under treatment. We have observed that our system exhibits two types of multi-soliton structures: the dark solitons and the bright solitons. The observed bright multi-solitons have different amplitudes. Low-amplitude multi-solitons are responsible for the transfer of signals or information through the molecule, while the high-amplitude soliton is responsible for the disaster/rescue process, hence the observed phase transition. Finally, we demonstrated that, from our studies, the fractional derivative order accelerated the migration of the breather, leading to a process called catastrophe/rescue.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Modified Slobodan–Zdravković model combined with fractional order and long-range interactions

  • 期刊论文

  • 发表日期：

    2026年4月15日

查看全文
  • Henock Ngoubi

摘要

The dynamics of the Slobodan–Zdravković (SZ) model was extended by simultaneously taking into account the fractional order e and the long-range interactions (LRI) of each dimer. We show that, the dynamics of the model is reduced to a nonlinear fractional Schrödinger equation, where the coefficients of dispersion and the nonlinearity depend strongly on the fractional derivative order parameter e and LRI coefficient s. We found that, for low values of s, the microtubules self-assemble and exhibit an unusual behaviour, undergoing alternating periods of growth and shrinkage (catastrophe), with rapid transitions between these states. The high values of s lead to the inverse process, known as rescue. Finally, one obtained the transition for high values of s. At this stage of high values of s, the wave amplitude decreases with time, showing that the system loses energy; therefore, the necessary information for the construction of proteins is lost. It turns out that the LRI is a valuable tool for monitoring the evolution of a biomolecular system, particularly when certain parameters change, such as under treatment. We have observed that our system exhibits two types of multi-soliton structures: the dark solitons and the bright solitons. The observed bright multi-solitons have different amplitudes. Low-amplitude multi-solitons are responsible for the transfer of signals or information through the molecule, while the high-amplitude soliton is responsible for the disaster/rescue process, hence the observed phase transition. Finally, we demonstrated that, from our studies, the fractional derivative order accelerated the migration of the breather, leading to a process called catastrophe/rescue.