Algorithms for Obtaining a Saddle Torus Between Two Attractors

Kamiyama, Kyohei; Komuro, M.; Endo, Tetsuro

doi:10.1142/s0218127413300322

Cited by 15 publications

(6 citation statements)

References 8 publications

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“…Studying bifurcations of quasi-periodic solutions using the methods in [37,38] is an open problem that we are tackling. Also, we are studying systems with different network structures (different numbers of neurons and reconnecting synapses).…”

Section: Resultsmentioning

confidence: 99%

Firing Patterns in Coupled Systems of Inhibitory Neurons

Kato

Kohno

2016

Journal of Signal Processing

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We investigate synchronization in neuronal networks with a small-world-like structure. Inhibitory connected neurons are considered. In a previous study, we found an interesting quasi-periodic solution such that neurons are classified into three groups: two groups with distinct firing rates and one group with only subthreshold oscillations. In this paper, we study its generation mechanism in the smallest system in which we can reconnect one synapse. As a result, we obtain the following mechanism: (1) non-uniformity of the firing frequency appears as a result of asymmetrical coupling, (2) neurons with a higher firing frequency suppress neurons with a lower firing frequency for an appropriate coupling coefficient, (3) three clustered states, that is, neurons with firing frequencies A and B (A/B is irrational) and neurons that do not fire, are generated. We also confirm this mechanism in a large population.

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Section: Resultsmentioning

confidence: 99%

Firing Patterns in Coupled Systems of Inhibitory Neurons

Kato

Kohno

2016

Journal of Signal Processing

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“…The unstable QPO is numerically estimated by the bisection method. 13 We numerically verify that the unstable orbit obtained by the bisection method is quasiperiodic. Using the unstable QPO, we choose the delay d ¼ 59 in which the average of the difference jjx nÀd À x n jj is sufficiently small (%3.65 Â 10 À3 ).…”

Section: Stabilization Of Unstable Qpo By Dfcmentioning

confidence: 94%

Delayed feedback control and phase reduction of unstable quasi-periodic orbits

Ichinose

Komuro

2014

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The delayed feedback control (DFC) is applied to stabilize unstable quasi-periodic orbits (QPOs) in discrete-time systems. The feedback input is given by the difference between the current state and a time-delayed state in the DFC. However, there is an inevitable time-delay mismatch in QPOs. To evaluate the influence of the time-delay mismatch on the DFC, we propose a phase reduction method for QPOs and construct a phase response curve (PRC) from unstable QPOs directly. Using the PRC, we estimate the rotation number of QPO stabilized by the DFC. We show that the orbit of the DFC is consistent with the unstable QPO perturbed by a small state difference resulting from the time-delay mismatch, implying that the DFC can certainly stabilize the unstable QPO.

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“…This technique of searching for an initial approximation for attractors of a system with slow variables (frequencies) goes back to the classical approaches [32,33] and is used in many problems of mechanics [34]. We note the demand for methods using the numerical continuation of such approximations in terms of parameters: there are various options, for example, [35,36].…”

Section: Steady Operating Modesmentioning

confidence: 99%

“…For the numerical verification of the existence of such a solution, we can apply the method [35,36]; however, this is a resource-intensive approach that goes beyond the scope of this study. We will restrict ourselves to an attempt to stabilize the solution, the existence of which we assume.…”

Section: Attractors Of a Complete Dynamical System: Approximations And Numerical Researchmentioning

confidence: 99%

Darrieus-Magnus Type Wind Turbine: Dynamics and Control

Климина

2021

J. Comput. Syst. Sci. Int.

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When the Darrieus rotor rotates, a force is generated that is akin to the Magnus force: perpendicular to the oncoming flow velocity. In this study, it is calculated based on a quasi-static model of the aerodynamic action and compared with a similar force acting on the Savonius rotor. This force allows the Darrieus rotor to be used as an element of a wind power plant operating based on the Magnus effect. The mathematical model of such a wind turbine with a horizontal shaft and two rotating blades in the form of Darrieus rotors is presented in the form of a fifth-order dynamic system. The parameter that characterizes the useful external electrical load in the local circuit of the electric generator of the plant acts as the gain of the control action in the model. As a result of the analysis, it is found that a wind turbine can have at least three types of operating modes. Two of them are characterized by the synchronization of the average angular velocities of the Darrieus rotors; in the general case, the average rotation speed of the central shaft is incommensurable with them. In the third type of modes, the proper rotation speeds of Darrieus rotors are incommensurable. The problem of choosing a control that provides the maximum value of mechanical power in the operating mode of the wind turbine is solved.

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Algorithms for Obtaining a Saddle Torus Between Two Attractors

Cited by 15 publications

References 8 publications

Firing Patterns in Coupled Systems of Inhibitory Neurons

Firing Patterns in Coupled Systems of Inhibitory Neurons

Delayed feedback control and phase reduction of unstable quasi-periodic orbits

Darrieus-Magnus Type Wind Turbine: Dynamics and Control

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