A Method of Solution for Resonant Nonlinear Coupled Oscillator Systems

1966 ◽  
Vol 7 (2) ◽  
pp. 399-403 ◽  
Author(s):  
John Waters ◽  
Joseph Ford
Keyword(s):  
Coupled Oscillator ◽  
Method Of Solution ◽  
Coupled Oscillator Systems

Delay stabilization of periodic orbits in coupled oscillator systems

2010 ◽  
Vol 368 (1911) ◽  
pp. 319-341 ◽  
Author(s):  
B. Fiedler ◽  
V. Flunkert ◽  
P. Hövel ◽  
E. Schöll
Keyword(s):  
Normal Form ◽  
Numerical Simulations ◽  
Periodic Orbits ◽  
Coupled Oscillators ◽  
Coupled Oscillator ◽  
Non Invasive ◽  
Coupling Parameters ◽  
Necessary And Sufficient ◽  
Time Delayed Feedback ◽  
Coupled Oscillator Systems

We study diffusively coupled oscillators in Hopf normal form. By introducing a non-invasive delay coupling, we are able to stabilize the inherently unstable anti-phase orbits. For the super- and subcritical cases, we state a condition on the oscillator’s nonlinearity that is necessary and sufficient to find coupling parameters for successful stabilization. We prove these conditions and review previous results on the stabilization of odd-number orbits by time-delayed feedback. Finally, we illustrate the results with numerical simulations.

NEURONAL OSCILLATIONS AND STOCHASTIC LIMIT CYCLES

1996 ◽  
Vol 07 (04) ◽  
pp. 399-402 ◽  
Author(s):  
CHRISTIAN KURRER ◽  
KLAUS SCHULTEN
Keyword(s):  
Nonlinear Dynamics ◽  
Limit Cycles ◽  
Neural Activity ◽  
Oscillatory Behavior ◽  
Neuronal Oscillations ◽  
Coupled Oscillator ◽  
Stochastic Limit ◽  
Excitable Systems ◽  
The Individual ◽  
Coupled Oscillator Systems

We investigate a model for synchronous neural activity in networks of coupled neurons. The individual systems are governed by nonlinear dynamics and can continuously vary between excitable and oscillatory behavior. Analytical calculations and computer simulations show that coupled excitable systems can undergo two different phase transitions from synchronous to asynchronous firing behavior. One of the transitions is akin to the synchronization transitions in coupled oscillator systems, while the second transition can only be found in coupled excitable systems. Using the concept of Stochastic Limit Cycles, we present an analytical derivation of the two transitions and discuss implications for synchronization transitions in biological neural networks.

Noise-induced transitions in coupled oscillator systems with a pinning force

1996 ◽  
Vol 54 (6) ◽  
pp. 6042-6052 ◽  
Author(s):  
Seunghwan Kim ◽  
Seon Hee Park ◽  
Chang Su Ryu
Keyword(s):  
Pinning Force ◽  
Coupled Oscillator ◽  
Coupled Oscillator Systems
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