Scholarlink

<p>In this investigation, we present a new variant of the classic Lorenz system, in which the sigma parameter is modelled as a rational quadratic function dependent on the variable <i>x</i> in the phase space. This modification induces new equilibria, which we denominate <i>induced equilibria</i>, and it originates two dynamic systems that share the same set of equilibrium points. One of these systems generates chaos with properties similar to the Lorenz system, with a 2-scroll structure but a different distribution of the chaos in the parameter space. In the second system, we highlight the multi-stability and its basins of fractal attraction, emphasizing how the modification of a parameter significantly alters the dynamics of the Lorenz system. We investigate the chaotic behaviour by means of the calculations of the Lyapunov exponents, presenting colour maps that illustrate regions of chaotic behaviour. Our study reveals the capacity of the modified system to exhibit rich and complex dynamic behaviours, highlighting the multi-stability by adding <i>equilibria</i> to a dynamic system.</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

Induced equilibria in the classical Lorenz system by means of a quadratic rational function

  • 期刊论文

  • 发表日期：

    2025年3月6日

查看全文
  • Juan José Rivas-Ramírez,
  • Joaquin Estevez-Delgado

摘要

In this investigation, we present a new variant of the classic Lorenz system, in which the sigma parameter is modelled as a rational quadratic function dependent on the variable x in the phase space. This modification induces new equilibria, which we denominate induced equilibria, and it originates two dynamic systems that share the same set of equilibrium points. One of these systems generates chaos with properties similar to the Lorenz system, with a 2-scroll structure but a different distribution of the chaos in the parameter space. In the second system, we highlight the multi-stability and its basins of fractal attraction, emphasizing how the modification of a parameter significantly alters the dynamics of the Lorenz system. We investigate the chaotic behaviour by means of the calculations of the Lyapunov exponents, presenting colour maps that illustrate regions of chaotic behaviour. Our study reveals the capacity of the modified system to exhibit rich and complex dynamic behaviours, highlighting the multi-stability by adding equilibria to a dynamic system.