A fractional-order ship power system: chaos and its dynamical properties
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Karthikeyan Rajagopal
,
Prakash Duraisamy
and
Iqtadar Hussain
Abstract
In this research, the ship power system is studied with a fractional-order approach. A 2-D model of a two-generator parallel-connected is considered. A chaotic attractor is observed for particular parameter values. The fractional-order form is calculated with the Adam–Bashforth–Moulton method. The chaotic response is identified even for the order 0.99. Phase portrait is generated using the Caputo derivative approach. Wolf’s algorithm is used to calculate Lyapunov exponents. For the considered values of parameters, one positive Lyapunov exponent confirms the existence of chaos. Bifurcation diagrams are presented to analyze the various dynamical behaviors and bifurcation points. Interestingly, the considered system is multistable. Also, antimonotonicity, period-doubling, and period halving are observed in the bifurcation diagram. As the last step, a fractional-order controller is designed to remove chaotic dynamics. Time plots are simulated to show the effectiveness of the controller.
Funding source: Chennai Institute of Technology
Award Identifier / Grant number: CIT/CNS/2020/RD/063
Acknowledgment
This work is partially funded by the Center for Nonlinear Systems, Chennai Institute of Technology, India vide funding number CIT/CNS/2020/RD/063
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: This work is funded by the Center for Nonlinear Systems, Chennai Institute of Technology, India vide funding number CIT/CNS/2020/RD/063.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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Articles in the same Issue
- Frontmatter
- Original Research Articles
- Coordinated target tracking in sensor networks by maximizing mutual information
- Legendre wavelet residual approach for moving boundary problem with variable thermal physical properties
- Computational study of intravenous magnetic drug targeting using implanted magnetizable stent
- Extended logistic map for encryption of digital images
- Valuation of the American put option as a free boundary problem through a high-order difference scheme
- Power minimization of gas transmission network in fully transient state using metaheuristic methods
- A priori error estimates for finite element approximations to transient convection-diffusion-reaction equations in fluidized beds
- Higher order rogue waves for the(3 + 1)-dimensional Jimbo–Miwa equation
- Dynamic characteristics of supersonic turbulent free jets from four types of circular nozzles
- New insights into singularity analysis
- Chaos and bifurcations in a discretized fractional model of quasi-periodic plasma perturbations
- Wavelet collocation methods for solving neutral delay differential equations
- Numerical solution of highly non-linear fractional order reaction advection diffusion equation using the cubic B-spline collocation method
- Solving nonlinear third-order boundary value problems based-on boundary shape functions
- Positive radial solutions for Dirichlet problems involving the mean curvature operator in Minkowski space
- Effect of outlet impeller diameter on performance prediction of centrifugal pump under single-phase and cavitation flow conditions
- A fractional-order ship power system: chaos and its dynamical properties
- Graphical structure of extended b-metric spaces: an application to the transverse oscillations of a homogeneous bar
- Hypergeometric fractional derivatives formula of shifted Chebyshev polynomials: tau algorithm for a type of fractional delay differential equations
- Modelling and numerical synchronization of chaotic system with fractional-order operator
