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Birkhoff Normal Forms and KAM Theory for Gumowski-Mira Equation [PDF]
The Scientific World Journal, 2014 By using the KAM theory we investigate the stability of equilibrium solutions of the Gumowski-Mira equation: xn+1=(2axn)/(1+xn2)-xn-1, n=0,1,…, where x-1,x0∈(-∞,∞), and we obtain the Birkhoff normal forms for this equation for different equilibrium ...
M. R. S. Kulenović +2 more
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The use of normal forms for analysing nonlinear mechanical vibrations [PDF]
Philosophical Transactions Series A, Mathematical, Physical, and Engineering Sciences, 2015 Alan Champneys, Tom Hill, David Wagg
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Van der Pol Equation with a Large Feedback Delay
Mathematics, 2023 The well-known Van der Pol equation with delayed feedback is considered. It is assumed that the delay factor is large enough. In the study of the dynamics, the critical cases in the problem of the stability of the zero equilibrium state are identified ...
Sergey Kashchenko
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On the Double-Zero Bifurcation of Jerk Systems
Mathematics, 2023 In this paper, we construct approximate normal forms of the double-zero bifurcation for a two-parameter jerk system exhibiting a non-degenerate fold bifurcation.
Cristian Lăzureanu
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Asymptotics of Regular and Irregular Solutions in Chains of Coupled van der Pol Equations
Mathematics, 2023 Chains of coupled van der Pol equations are considered. The main assumption that motivates the use of special asymptotic methods is that the number of elements in the chain is sufficiently large.
Sergey Kashchenko
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Approximate Nonlinear Discrete-Time Models Based on B-Spline Functions
IEEE Access, 2020 We consider the discretization of continuous-time nonlinear systems described by normal forms. In particular, we consider the case when the input to the system is generated by a B-spline hold device to obtain an approximate discrete-time model.
Claudia Sanchez, Juan I. Yuz
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Relaxation Oscillations in the Logistic Equation with Delay and Modified Nonlinearity
Mathematics, 2023 We consider the dynamics of a logistic equation with delays and modified nonlinearity, the role of which is to bound the values of solutions from above.
Alexandra Kashchenko, Sergey Kashchenko
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Design system for normalization by Using Normal Forms
Tikrit Journal of Pure Science, 2023 Electronic learning is the use of modern technology of different types for information delivery in order to reduce both time and effort for maintaining a wide range of benefit through many patterns or programs like simulation which help the learner to ...
Elham hassan Aziz
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Normal Form and Solitons [PDF]
, 2008 32 pages, AMSLaTeX, 8 ...
Hiraoka, Y., Kodama, Y.
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Analytical Solution to Normal Forms of Hamiltonian Systems
Mathematical and Computational Applications, 2017 The idea of the normalisation of the Hamiltonian system is to simplify the system by transforming Hamiltonian canonically to an easy system. It is under symplectic conditions that the Hamiltonian is preserved under a specific transformation—the so-called
Ali Allahem
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