5 papers
Unbounded sequences of stable limit cycles in the delayed Duffing equation: an exact analysis
Si Mohamed Sah, Bernold Fiedler, B. Shayak +1
The delayed Duffing equation is shown to possess an infinite and unbounded sequence of rapidly oscillating, asymptotically stable periodic solutions,…
Coexistence of infinitely many large, stable, rapidly oscillating periodic solutions in time-delayed Duffing oscillators
Bernold Fiedler, Alejandro López Nieto, Richard H. Rand +3
We explore stability and instability of rapidly oscillating solutions for the hard spring delayed Duffing oscillator Fix . We target…
The Mathieu Differential Equation and Generalizations to Infinite Fractafolds
Shiping Cao, Anthony Coniglio, Xueyan Niu +2
One of the well-studied equations in the theory of ODEs is the Mathieu differential equation. A common approach for obtaining solutions is to seek solutions via Fourier series by c…
Limiting the Oscillations in Queues with Delayed Information Through a Novel Type of Delay Announcement
Sophia Novitzky, Jamol Pender, Richard Rand +1
Many service systems use technology to notify customers about their expected waiting times or queue lengths via delay announcements. However, in many cases, either the information…
Dynamics of Two Coupled van der Pol Oscillators with Delay Coupling Revisited
Mark Gluzman, Richard Rand
The problem of two van der Pol oscillators coupled by velocity delay terms was studied by Wirkus and Rand in 2002. The small-epsilon analysis resulted in a slow flow which containe…