Abstract
The fractional derivative is increasingly used in modeling of nonlinear systems. Fractional-order systems often give better fit to the experimental results, especially for the systems in which memory effects or hysteresis play a significant role. The paper presents numerical results obtained for Lorenz dynamical system, described by equations with the fractional derivative components. The impact of the fractional derivative terms on the system dynamics and stability is analyzed by using phase diagrams and recurrence plot analysis.
Highlights
The first mention of fractional calculus dates back 300 years
In the current paper, we focus on applying the recurrence quantification analysis (RQA) to study the influence of the fractional derivative on the nonlinear system dynamics
In these preliminary investigations we study the dynamics of the system when the fractional derivative appears only in the first equation
Summary
The first mention of fractional calculus dates back 300 years. The idea of fractional derivative began to appear in conversations and correspondence between different scientists including. The use of fractional calculus in various fields of knowledge has been developed One can find their application in bioengineering [2], heat transfer [3], energy harvesting [4, 5], nonlinear dynamics [6], and many others. Differential equations with the fractional derivative are well suitable for modeling of many real systems. This means that in nature the ’fractional’ dynamics is common and should be considered in the scientific research. The influence of the fractional derivative on the dynamics of a nonlinear system is an interesting research topic, especially, as a method of studying real systems and phenomena. The observed regularities and dependencies are discussed and summarize in the last section
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