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Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 06/2015, Volume 426, Issue 2, pp. 995 - 1011
Conditions are given for the existence of a solution of given period to the impulsively driven van der Pol equation. Results are obtained for impulses of... 
State dependent impulses | Functions of bounded variation | Generalized functions | Periodic solutions | Van der Pol's equation | Contraction principle | MATHEMATICS, APPLIED | 2ND ORDER | LINEAR DIFFERENTIAL EQUATIONS | VARIABLE MOMENTS | MATHEMATICS | OSCILLATIONS | DELAY
Journal Article
Nonlinear Dynamics, ISSN 0924-090X, 8/2011, Volume 65, Issue 3, pp. 247 - 254
Journal Article
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 12/2013, Volume 18, Issue 12, pp. 3575 - 3589
•Three generalizations of the van der Pol equation (VDPE) using three newly proposed generalized operators are presented.•These operators allow kernels to be... 
Generalized operators | Numerical solution | Limit cycle | Fractional calculus | van der Pol equation | Van der Pol equation | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PHYSICS, FLUIDS & PLASMAS | DYNAMICS | PHYSICS, MATHEMATICAL | Differential equations
Journal Article
Journal of Vibration and Control, ISSN 1077-5463, 12/2012, Volume 18, Issue 14, pp. 2201 - 2209
Journal Article
Electronic Journal of Differential Equations, ISSN 1072-6691, 05/2014, Volume 2014, Issue 120, pp. 1 - 22
In this article, we study the bifurcation of limit cycles from the harmonic oscillator x = y, y = -x in the system x = y, y = -x + epsilon f(y) (1 - x(2)),... 
Sinusoidal-type number | Generalized Van der Pol equation | Hilbert's 16th problem | Sinusoidal-type set | Dependent radius | Lambda-point | Limit cycle | Existence | MATHEMATICS, APPLIED | sinusoidal-type set | NUMBER | existence | MATHEMATICS | limit cycle | LIENARD EQUATIONS | sinusoidal-type number | LIMIT-CYCLES | dependent radius | lambda-point
Journal Article
The European Physical Journal Special Topics, ISSN 1951-6355, 9/2019, Volume 228, Issue 9, pp. 1839 - 1854
In this paper, nonlinear frequency-amplitude characteristics of periodic motions in a periodically forced van der Pol oscillator are studied systematically.... 
Condensed Matter Physics | Measurement Science and Instrumentation | Materials Science, general | Classical and Continuum Physics | Atomic, Molecular, Optical and Plasma Physics | Physics, general | Physics | GENERALIZED NONLINEAR VAN | SCHEME | DIFFERENTIAL-EQUATIONS | LIMIT-CYCLE | PHYSICS, MULTIDISCIPLINARY
Journal Article
Journal Article
by He, Lei and Yi, Li and Tang, Pei
Advances in Difference Equations, ISSN 1687-1839, 12/2016, Volume 2016, Issue 1, pp. 1 - 11
Journal Article
Electronic Journal of Differential Equations, ISSN 1072-6691, 01/2014, Volume 2014, Issue 22, pp. 1 - 9
In this article, we study the bifurcation of limit cycles from the linear oscillator x = y, y = -x in the class x = y, = -x + Ey(P+1) (1-x(2q)), where E is a... 
Limit cycles | Generalized Van der Pol equation | Existence | Uniqueness | MATHEMATICS | MATHEMATICS, APPLIED | existence | uniqueness | limit cycles
Journal Article
Abstract and Applied Analysis, ISSN 1085-3375, 2014, Volume 2014, pp. 1 - 10
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 10/2016, Volume 261, Issue 7, pp. 4164 - 4187
Subject to a priori bounds, Liénard equations with state dependent impulsive forcing are shown to admit a unique absolutely continuous anti-periodic solution... 
State dependent impulses | Josephson's equation | Generalized functions | Anti-periodic solutions | Liénard equations | van der Pol's equation | PERIODIC-SOLUTIONS | VAN | Lienard equations | BOUNDARY-VALUE-PROBLEMS | BVPS | 2ND ORDER | VARIABLE MOMENTS | MATHEMATICS | 1ST-ORDER DIFFERENTIAL-EQUATIONS | DELAY EQUATIONS | POL EQUATION | OSCILLATIONS
Journal Article
Journal of Computational and Nonlinear Dynamics, ISSN 1555-1415, 07/2016, Volume 11, Issue 4, pp. 041030 - 041030-5
This study aims to investigate the harmonic resonance of third-order forced van der Pol oscillator with fractional-order derivative using the asymptotic... 
fractional-order derivative | amplitude-frequency curves | van der Pol oscillator | harmonic resonance | asymptotic method | GENERALIZED VAN | CHAOS | MECHANICS | CALCULUS | DYNAMIC PROBLEMS | ENGINEERING, MECHANICAL | Nonlinear dynamics | Harmonics | Mathematical analysis | Mathematical models | Derivatives | Dynamical systems | Asymptotic methods | Oscillators
Journal Article
Applied and Computational Mechanics, ISSN 1802-680X, 2018, Volume 12, Issue 1, pp. 45 - 58
The paper is motivated by a series of wind tunnel experiments, which deal with aeroelastic Single Degree of Freedom (SDOF) and Two Degrees of Freedom (TDOF)... 
Generalized van der pol system | Limit cycles | Stochastic stability | Stochastic averaging | stochastic stability | stochastic averaging | generalized van der Pol system | limit cycles
Journal Article
Nonlinear Dynamics, ISSN 0924-090X, 8/2017, Volume 89, Issue 3, pp. 2103 - 2114
Journal Article
International Journal of Non-Linear Mechanics, ISSN 0020-7462, 05/2020, Volume 121, p. 103441
A generalized two-degree-of-freedom non-linear mathematical system with non-linear gyroscopic and non-conservative terms was used to set up a model for heave... 
Routh–Hurwitz conditions | Generalized van der Pol equation | Instability | Flutter | Non-linear aero-elastic system
Journal Article
Qualitative Theory of Dynamical Systems, ISSN 1575-5460, 10/2016, Volume 15, Issue 2, pp. 349 - 365
In this paper global bifurcations for a class of planar Filippov systems with symmetry, namely the Filipov-van der Pol oscillator are studied. First, we... 
Global phase portrait | van der Pol oscillator | Generalized Hopf bifurcation | 34C23 | 49J52 | Difference and Functional Equations | Mathematics, general | Mathematics | Dynamical Systems and Ergodic Theory | Filippov system | Limit cycle | 34C07 | MATHEMATICS | MATHEMATICS, APPLIED | HOPF BIFURCATIONS | PIECEWISE-SMOOTH | FLOWS
Journal Article
Tianjin Daxue Xuebao (Ziran Kexue yu Gongcheng Jishu Ban)/Journal of Tianjin University Science and Technology, ISSN 0493-2137, 09/2018, Volume 51, Issue 9, pp. 895 - 902
Journal Article
Nonlinear Dynamics, ISSN 0924-090X, 05/2016, Volume 84, Issue 3, pp. 1201 - 1223
Journal Article
Abstract and Applied Analysis, ISSN 1085-3375, 2013, Volume 2013, pp. 1 - 8
Fuzzy electronic circuit (FEC) is firstly introduced, which is implementing Takagi-Sugeno (T-S) fuzzy chaotic systems on electronic circuit. In the research... 
MATHEMATICS, APPLIED | NETWORK | POL SYSTEMS | CONTROLLER | GENERALIZED SYNCHRONIZATION | MATHIEU-VAN | STABILITY | IMPLEMENTATION | CHEN-LEE SYSTEM | MODEL | FUNCTIONAL SYSTEM | Fuzzy logic | Engineering research | Chaos theory | Mathematical research | Fuzzy algorithms | Research | Properties | Electronic circuits | Fuzzy systems | Studies | Ordinary differential equations | Behavior | Agreements
Journal Article
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