Stability chart for the delayed Mathieu equation

By Tamás Insperger, Gábor Stépán. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2002

89 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0dd29c350f576b802943f8a18f2b8a54d9e1a2f0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Tamás Insperger
2. Richard H. Rand
3. Gábor Stépán
4. Brian P. Mann
5. B. Patel
6. T. Morrison
7. S. Sah
8. Ivana Kovacic

In Computer Networks and Communications

1. Tamás Insperger
2. Brian P. Mann
3. B. Patel
4. Gábor Stépán
5. Richard H. Rand
6. S. Sah
7. Ivana Kovacic
8. T. Morrison

In Statistical and Nonlinear Physics

1. Tamás Insperger
2. Richard H. Rand
3. Brian P. Mann
4. Gábor Stépán
5. T. Morrison
6. B. Patel
7. S. Sah
8. Ivana Kovacic

Citations in the corpus

• Stability of linear time‐periodic delay‐differential equations via Chebyshev polynomials (2004, methodology): “This is similar to the approach used in Reference [25] for time-periodic ODEs.”
• Stability of Delay Equations Written as State Space Models (2010, methodology): “Insperger and Stépán (2001b, 2002b, 2004) used an analytical and semi-discretization approach and Garg et al. (2007) used a second-order TFEA to investigate the stability of the DDME.”
• On the higher-order semi-discretizations for periodic delayed systems (2008, unknown): “[14].”
• 2:1 Resonance in the delayed nonlinear Mathieu equation (2007, methodology): “In this section, we compare the foregoing analytical results based on the slow flow (13) and (14) or (15) and (16), with direct numerical integration of the delayed Mathieu Equation (2).”
• Updated semi‐discretization method for periodic delay‐differential equations with discrete delay (2004, methodology): “This case is clear and the stability charts are known in closed form [33, 34].”
• Mathieu's Equation and Its Generalizations: Overview of Stability Charts and Their Features (2018, methodology): “[33] by utilizing the method of exponential multipliers.”
• Act-and-wait control concept for discrete-time systems with feedback delay (2007, background): “Equation (7) yields the characteristic equation μ + n ∑”
• Semi‐discretization method for delayed systems (2002, methodology): “Insperger and St ep an [28] also used Hill’s method to determine the closed-form stability chart for the Mathieu equation with one discrete delay.”