scholarly journals Discretization analysis of bifurcation based nonlinear amplifiers

2017 ◽  
Vol 15 ◽  
pp. 43-47
Author(s):  
Sven Feldkord ◽  
Marco Reit ◽  
Wolfgang Mathis
Keyword(s):  
Hopf Bifurcation ◽  
Numerical Integration ◽  
Discrete Time ◽  
Continuous Time ◽  
Higher Order ◽  
Qualitative Behavior ◽  
Discrete Time System ◽  
Integration Methods ◽  
Numerical Integration Methods ◽  
Nonlinear Amplifiers

Abstract. Recently, for modeling biological amplification processes, nonlinear amplifiers based on the supercritical Andronov–Hopf bifurcation have been widely analyzed analytically. For technical realizations, digital systems have become the most relevant systems in signal processing applications. The underlying continuous-time systems are transferred to the discrete-time domain using numerical integration methods. Within this contribution, effects on the qualitative behavior of the Andronov–Hopf bifurcation based systems concerning numerical integration methods are analyzed. It is shown exemplarily that explicit Runge–Kutta methods transform the truncated normalform equation of the Andronov–Hopf bifurcation into the normalform equation of the Neimark–Sacker bifurcation. Dependent on the order of the integration method, higher order terms are added during this transformation.A rescaled normalform equation of the Neimark–Sacker bifurcation is introduced that allows a parametric design of a discrete-time system which corresponds to the rescaled Andronov–Hopf system. This system approximates the characteristics of the rescaled Hopf-type amplifier for a large range of parameters. The natural frequency and the peak amplitude are preserved for every set of parameters. The Neimark–Sacker bifurcation based systems avoid large computational effort that would be caused by applying higher order integration methods to the continuous-time normalform equations.

scholarly journals Symplectic Integrators for Hamiltonian Systems: Basic Theory

1992 ◽  
Vol 152 ◽  
pp. 407-411 ◽  
Author(s):  
Haruo Yoshida
Keyword(s):  
Numerical Integration ◽  
Hamiltonian Systems ◽  
Higher Order ◽  
Basic Theory ◽  
Conserved Quantity ◽  
Symplectic Integrators ◽  
Integration Methods ◽  
Numerical Integration Methods ◽  
Secular Increase

Symplectic integrators are numerical integration methods for Hamiltonian systems, which conserves the symplectic 2-form exactly. With use of symplectic integrators there is no secular increase in the error of the energy because of the existence of a conserved quantity closed to the original Hamiltonian. Higher order symplectic integrators are obtained by a composition of 2nd order ones.

Stability of real-time hybrid simulation involving time-varying delay and direct integration algorithms

2021 ◽  
pp. 107754632110016
Author(s):  
Liang Huang ◽  
Cheng Chen ◽  
Shenjiang Huang ◽  
Jingfeng Wang
Keyword(s):  
Real Time ◽  
Discrete Time ◽  
Continuous Time ◽  
Hybrid Simulation ◽  
Time Varying ◽  
Discrete Time System ◽  
Time System ◽  
Integration Algorithms ◽  
The Stability ◽  
Continuous Time System

Stability presents a critical issue for real-time hybrid simulation. Actuator delay might destabilize the real-time test without proper compensation. Previous research often assumed real-time hybrid simulation as a continuous-time system; however, it is more appropriately treated as a discrete-time system because of application of digital devices and integration algorithms. By using the Lyapunov–Krasovskii theory, this study explores the convoluted effect of integration algorithms and actuator delay on the stability of real-time hybrid simulation. Both theoretical and numerical analysis results demonstrate that (1) the direct integration algorithm is preferably used for real-time hybrid simulation because of its computational efficiency; (2) the stability analysis of real-time hybrid simulation highly depends on actuator delay models, and the actuator model that accounts for time-varying characteristic will lead to more conservative stability; and (3) the integration step is constrained by the algorithm and structural frequencies. Moreover, when the step is small, the stability of the discrete-time system will approach that of the corresponding continuous-time system. The study establishes a bridge between continuous- and discrete-time systems for stability analysis of real-time hybrid simulation.

scholarly journals On the relationship between long-period comets and large trans-Neptunian planetary bodies

2016 ◽  
Vol 12 (S325) ◽  
pp. 263-265
Author(s):  
Rustam Guliyev ◽  
Ayyub Guliyev
Keyword(s):  
Solar System ◽  
Numerical Integration ◽  
Dynamical Evolution ◽  
Integration Methods ◽  
Long Period ◽  
Planetary Bodies ◽  
Numerical Integration Methods ◽  
Relationship Of ◽  
The Relationship

AbstractIn the present work we investigate the possible relationship of long-period comets with five large and distant trans-Neptunian bodies (Sedna, Eris, 2007 OR10, 2012 VP113and 2008 ST291) in order to determine the probability of the transfer of a part of these kind of comets to the inner of the Solar System. To identify such relationships, we studied the relative positions of the comet orbits and listed TNOs. Using numerical integration methods, we examined dynamical evolution of the comets and have found one encounter of comet C/1861J1 and Eris.

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