The Experts below are selected from a list of 38598 Experts worldwide ranked by ideXlab platform
Arkady Pikovsky - One of the best experts on this subject based on the ideXlab platform.
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numerical phase reduction beyond the first order approximation
Chaos, 2019Co-Authors: Michael Rosenblum, Arkady PikovskyAbstract:We develop a numerical approach to reconstruct the phase dynamics of driven or coupled self-sustained oscillators. Employing a simple algorithm for computation of the phase of a Perturbed System, we construct numerically the equation for the evolution of the phase. Our simulations demonstrate that the description of the dynamics solely by phase variables can be valid for rather strong coupling strengths and large deviations from the limit cycle. Coupling functions depend crucially on the coupling and are generally non-decomposable in phase response and forcing terms. We also discuss the limitations of the approach.
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numerical phase reduction beyond the first order approximation
arXiv: Computational Physics, 2018Co-Authors: Michael Rosenblum, Arkady PikovskyAbstract:We develop a numerical approach to reconstruct the phase dynamics of driven or coupled self-sustained oscillators. Employing a simple algorithm for computation of the phase of a Perturbed System, we construct numerically the equation for the evolution of the phase. Our simulations demonstrate that the description of the dynamics solely by phase variables can be valid for rather strong coupling strengths and large deviations from the limit cycle. Coupling functions depend crucially on the coupling and are generally non-decomposable in phase response and forcing terms. We also discuss limitations of the approach.
Srinivasan Natesan - One of the best experts on this subject based on the ideXlab platform.
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a uniformly convergent numerical scheme for a coupled System of singularly Perturbed reaction diffusion equations
Numerical Functional Analysis and Optimization, 2020Co-Authors: Gautam Singh, Srinivasan NatesanAbstract:Here, we study the numerical solution of singularly Perturbed System of two-point boundary-value problems of reaction-diffusion type. The solutions of these problems exhibit twin overlapping expone...
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a uniformly convergent nipg method for a singularly Perturbed System of reaction diffusion boundary value problems
International Conference on Mathematics and Computing, 2018Co-Authors: Gautam Singh, Srinivasan NatesanAbstract:In this article, we study the numerical solution of singularly Perturbed System of boundary-value problems for second-order ordinary differential equations of reaction–diffusion type. The solution of these problems exhibits twin boundary layers at both the ends of the domain. To obtain the numerical solution of these problems, we apply the nonsymmetric discontinuous Galerkin FEM with interior penalties (NIPG method). Also, we proved that the method is \(O(N^{-1}\ln N)^{k}\) accurate in energy norm, on Shishkin mesh with N number of intervals and k degree of piecewise polynomial. Numerical results are presented to support the theoretical results.
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optimal error estimate using mesh equidistribution technique for singularly Perturbed System of reaction diffusion boundary value problems
Applied Mathematics and Computation, 2014Co-Authors: Srinivasan NatesanAbstract:In this article, we study the problem of determining an appropriate grading of meshes for a System of coupled singularly Perturbed reaction-diffusion problems having diffusion parameters with different magnitudes. The central difference scheme is used to discretize the problem on adaptively generated mesh where the mesh equation is derived using an equidistribution principle. An a priori monitor function is obtained from the error estimate. A suitable a posteriori analogue of this monitor function is also derived for the mesh construction which will lead to an optimal second-order parameter uniform convergence. We present the results of numerical experiments for linear and semilinear reaction-diffusion Systems to support the effectiveness of our preferred monitor function obtained from theoretical analysis.
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a uniformly convergent hybrid scheme for singularly Perturbed System of reaction diffusion robin type boundary value problems
Journal of Applied Mathematics and Computing, 2013Co-Authors: Pratibhamoy Das, Srinivasan NatesanAbstract:This paper deals with the study on System of reaction diffusion differential equations for Robin or mixed type boundary value problems (MBVPs). A cubic spline approximation has been used to obtain the difference scheme for the System of MBVPs, on a piecewise uniform Shishkin mesh defined in the whole domain. It has been shown that our proposed scheme, i.e., central difference approximation for outer region with cubic spline approximation for inner region of boundary layers, leads to almost second order parameter uniform convergence whereas the standard method i.e., the forward-backward approximation for mixed boundary conditions with central difference approximation inside the domain leads to almost first order convergence on Shishkin mesh. Numerical results are provided to show the efficiency and accuracy of these methods.
Emilia Fridman - One of the best experts on this subject based on the ideXlab platform.
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stability of Systems with uncertain delays a new complete lyapunov krasovskii functional
IEEE Transactions on Automatic Control, 2006Co-Authors: Emilia FridmanAbstract:Stability of linear Systems with uncertain time-varying delay is considered in the case, where the nominal value of the delay is constant and nonzero. Recently a new construction of Lyapunov-Krasovskii functionals (LKFs) has been introduced: To a nominal LKF, which is appropriate to the System with nominal delays, terms are added that correspond to the Perturbed System and that vanish when the delay perturbations approach 0. In the present note we combine a "complete" nominal LKF, the derivative of which along the trajectories depends on states and their derivatives, with the additional terms depending on the delay perturbation. The new method is applied to the case of multiple uncertain delays with one nonzero nominal value. Numerical examples illustrate the efficiency of the method.
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brief a descriptor System approach to nonlinear singularly Perturbed optimal control problem
Automatica, 2001Co-Authors: Emilia FridmanAbstract:This paper considers the infinite horizon nonlinear quadratic optimal control problem for a singularly Perturbed System which is nonlinear in both, the slow and the fast variables. The relationship between this problem and the analogous one for a descriptor System is investigated. Parameter-independent controllers are constructed that solve the problem for the descriptor System and lead the full-order System to the near-optimal performance. Estimates on the closeness of the cost under near-optimal controllers to the optimal one are obtained.
Michael Rosenblum - One of the best experts on this subject based on the ideXlab platform.
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numerical phase reduction beyond the first order approximation
Chaos, 2019Co-Authors: Michael Rosenblum, Arkady PikovskyAbstract:We develop a numerical approach to reconstruct the phase dynamics of driven or coupled self-sustained oscillators. Employing a simple algorithm for computation of the phase of a Perturbed System, we construct numerically the equation for the evolution of the phase. Our simulations demonstrate that the description of the dynamics solely by phase variables can be valid for rather strong coupling strengths and large deviations from the limit cycle. Coupling functions depend crucially on the coupling and are generally non-decomposable in phase response and forcing terms. We also discuss the limitations of the approach.
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numerical phase reduction beyond the first order approximation
arXiv: Computational Physics, 2018Co-Authors: Michael Rosenblum, Arkady PikovskyAbstract:We develop a numerical approach to reconstruct the phase dynamics of driven or coupled self-sustained oscillators. Employing a simple algorithm for computation of the phase of a Perturbed System, we construct numerically the equation for the evolution of the phase. Our simulations demonstrate that the description of the dynamics solely by phase variables can be valid for rather strong coupling strengths and large deviations from the limit cycle. Coupling functions depend crucially on the coupling and are generally non-decomposable in phase response and forcing terms. We also discuss limitations of the approach.
A Goldenberge - One of the best experts on this subject based on the ideXlab platform.
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design of performance robustness for uncertain linear Systems with state and control delays
IEEE Transactions on Automatic Control, 1998Co-Authors: P P J Van Den Bosch, S Weiland, A GoldenbergeAbstract:The linear Systems considered in this paper are subject to uncertain perturbations of norm-bounded time-varying parameters and multiple time delays in System state and control. The time delays are uncertain, independent of each other, and allowed to be time-varying. The integral quadratic cost criterion is employed to measure System performance. Using solutions of Lyapunov and Riccati equations, a linear state feedback control law is proposed to stabilize the Perturbed System and to guarantee an upper bound of System performance, which is applicable to arbitrary time delays.