Search results for "Fractional-order system"

showing 4 items of 4 documents

Fractional-Order System Identification of Viscoelastic Behavior: A Frequency Domain Based Experimental Study

2020

In this work, the fractional-order modeling of viscoelastic behavior is investigated based on measurement data in the frequency domain. For the results of two different test setups we apply existing parameter estimation algorithms designed for fractional-order transfer functions. These algorithms require a priori knowledge of the system structure including the commensurate order of differentiation. An iterative procedure is used to evaluate the influence of the unknown structure. The measured polymer samples show a viscoelastic stress response. We can show that integer-order models are not capable of capturing this behavior. For a set of predefined structures, the best obtained fractional-o…

0209 industrial biotechnologyComputer scienceFractional-order system02 engineering and technologyVariation of parametersTransfer functionViscoelasticitySet (abstract data type)Identification (information)020303 mechanical engineering & transports020901 industrial engineering & automation0203 mechanical engineeringFrequency domainA priori and a posterioriAlgorithm2020 IEEE 16th International Workshop on Advanced Motion Control (AMC)
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Coupled Discrete Fractional-Order Logistic Maps

2021

This paper studies a system of coupled discrete fractional-order logistic maps, modeled by Caputo’s delta fractional difference, regarding its numerical integration and chaotic dynamics. Some interesting new dynamical properties and unusual phenomena from this coupled chaotic-map system are revealed. Moreover, the coexistence of attractors, a necessary ingredient of the existence of hidden attractors, is proved and analyzed.

General Mathematicscaputo delta fractional differenceChaoticattraktoritstabilityStability (probability)fractional-order difference equationNumerical integrationNonlinear Sciences::Chaotic DynamicsAttractorQA1-939Computer Science (miscellaneous)Applied mathematicsOrder (group theory)dynaamiset systeemitEngineering (miscellaneous)Mathematicsdiscrete fractional-order systemhidden attractorMathematicsMathematics
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D3 Dihedral Logistic Map of Fractional Order

2021

In this paper, the D3 dihedral logistic map of fractional order is introduced. The map presents a dihedral symmetry D3. It is numerically shown that the construction and interpretation of the bifurcation diagram versus the fractional order requires special attention. The system stability is determined and the problem of hidden attractors is analyzed. Furthermore, analytical and numerical results show that the chaotic attractor of integer order, with D3 symmetries, looses its symmetry in the fractional-order variant.

kaaosteoriaGeneral Mathematicscomputational_mathematicscaputo delta fractional differencedihedral symmetry <i>D</i><sub>3</sub>attraktoritmatemaattinen analyysiNonlinear Sciences::Chaotic DynamicsbifurkaatioQA1-939Computer Science (miscellaneous)dihedral symmetry D3dynaamiset systeemitEngineering (miscellaneous)Mathematicsdiscrete fractional-order systemdiscrete fractional-order system; caputo delta fractional difference; hidden attractor; dihedral symmetry <i>D</i><sub>3</sub>hidden attractor
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Complex dynamics, hidden attractors and continuous approximation of a fractional-order hyperchaotic PWC system

2018

In this paper, a continuous approximation to studying a class of PWC systems of fractionalorder is presented. Some known results of set-valued analysis and differential inclusions are utilized. The example of a hyperchaotic PWC system of fractional order is analyzed. It is found that without equilibria, the system has hidden attractors.

likiarvotFOS: Physical sciencesAerospace EngineeringattraktoritOcean EngineeringDynamical Systems (math.DS)hidden chaotic attractor01 natural sciences010305 fluids & plasmasDifferential inclusion0103 physical sciencesAttractorFOS: MathematicsApplied mathematicsOrder (group theory)Mathematics - Dynamical Systemsdynaamiset systeemitElectrical and Electronic Engineering010301 acousticsMathematicskaaosteoriaContinuous approximationmurtoluvutperiodicity of fractional-order systemPWC system of fractional orderApplied MathematicsMechanical EngineeringNonlinear Sciences - Chaotic DynamicsNonlinear Sciences::Chaotic DynamicsComplex dynamicshyperchaosControl and Systems Engineeringcontinuous approximationapproksimointiChaotic Dynamics (nlin.CD)Nonlinear Dynamics
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