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Nonlinear Dynamics

, Volume 95, Issue 2, pp 1457–1470 | Cite as

Fractal analysis and control of the fractional Lotka–Volterra model

  • Yupin Wang
  • Shutang LiuEmail author
Original Paper
  • 164 Downloads

Abstract

This paper reports the investigation of a fractional Lotka–Volterra model from the fractal viewpoint. A Julia set of a discrete version of this model is introduced and its state feedback control is realized. Coupled terms are designed to realize the synchronization of two Julia sets with different parameters. Numerical simulations are presented to further verify the correctness and effectiveness of the main theoretical results.

Keywords

Fractional Lotka–Volterra system Discretization Julia set Feedback control Synchronization 

Mathematics Subject Classification

26A33 34K35 37P40 92D25 

Notes

Acknowledgements

This research is supported by the National Natural Science Foundation of China (No. 61533011). The authors sincerely thank the reviewers for their valuable suggestions and useful comments that have led to the present improved version of the original manuscript. The first author is also indebted to Dr. H. Li for numerous helpful discussions.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Human and animals rights

This article does not contain any studies with human participants or animals performed by any of the authors.

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Institute of Marine Science and Technology, Shandong UniversityJinanPeople’s Republic of China
  2. 2.School of Control Science and Engineering, Shandong UniversityJinanPeople’s Republic of China

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