Effects of periodic forcing on delayed bifurcations

1997 ◽  
Vol 9 (4) ◽  
pp. 561-625 ◽  
Author(s):  
Jianzhong Su
Keyword(s):  
Periodic Forcing ◽  
Delayed Bifurcations

Pathfollowing of high-dimensional hysteretic systems under periodic forcing

2021 ◽  
Author(s):  
Giovanni Formica ◽  
Nicoló Vaiana ◽  
Luciano Rosati ◽  
Walter Lacarbonara
Keyword(s):  
High Dimensional ◽  
Periodic Forcing ◽  
Hysteretic Systems

Spiral waves in excitable media due to noise and periodic forcing

2011 ◽  
Vol 44 (9) ◽  
pp. 728-738 ◽  
Author(s):  
Guoyong Yuan ◽  
Lin Xu ◽  
Aiguo Xu ◽  
Guangrui Wang ◽  
Shiping Yang
Keyword(s):  
Spiral Waves ◽  
Excitable Media ◽  
Periodic Forcing

Stirring Effect on the Belousov-Zhabotinsky Oscillating Chemical Reactions in a Batch. Experimental and Modelling

2010 ◽  
Vol 65 (1-2) ◽  
pp. 132-140 ◽  
Author(s):  
Yevhen Yu. Kalishyn ◽  
Małgorzata Rachwalska ◽  
Peter E. Strizhak
Keyword(s):  
Kinetic Scheme ◽  
Hopf Bifurcations ◽  
Hydrodynamic Turbulence ◽  
Stirring Rate ◽  
Diffusion Controlled ◽  
Stirring Effect ◽  
Delayed Bifurcations ◽  
Diffusion Controlled Reaction ◽  
Transient Oscillations ◽  
Good Agreement

AbstractWe have studied the stirring effect on the time-delayed bifurcations of transient oscillations in the Belousov-Zhabotinsky (BZ) oscillating chemical reaction in a closed system. Experiments show that oscillations disappear through the time-delayed Hopf bifurcations, whose parameters depend on the stirring rate. The explanation of the stirring effect is based on the theories of diffusion-controlled reactions and hydrodynamic turbulence. We show that an increase of the stirring rate leads to an increase of the rate constant for the diffusion-controlled reaction. We propose a kinetic scheme that describes the effect observed in the experiments. A good agreement between the experimental data and the simulations is obtained.

Control and managing of localized states in two-dimensional systems with periodic forcing

2010 ◽  
Vol 59 (1) ◽  
pp. 43-51 ◽  
Author(s):  
M. G. Clerc ◽  
F. Haudin ◽  
S. Residori ◽  
U. Bortolozzo ◽  
R. G. Rojas
Keyword(s):  
Localized States ◽  
Two Dimensional ◽  
Periodic Forcing

scholarly journals Periodic forcing of a K+ channel at various temperatures

1994 ◽  
Vol 66 (6) ◽  
pp. 1844-1852 ◽  
Author(s):  
D. Petracchi ◽  
M. Pellegrini ◽  
M. Pellegrino ◽  
M. Barbi ◽  
F. Moss
Keyword(s):  
K Channel ◽  
Periodic Forcing

Nonlinear Behavior of Sinusoidally Forced Pyloric Pacemaker Neurons

2001 ◽  
Vol 85 (4) ◽  
pp. 1623-1638 ◽  
Author(s):  
Attila Szűcs ◽  
Robert C. Elson ◽  
Michail I. Rabinovich ◽  
Henry D. I. Abarbanel ◽  
Allen I. Selverston
Keyword(s):  
Complex Dynamics ◽  
Cooperative Behavior ◽  
Model Neuron ◽  
Nonlinear Behavior ◽  
Periodic Forcing ◽  
Pacemaker Neurons ◽  
Strongly Coupled ◽  
Electronic Model ◽  
Group 2 ◽  
Low Dimensional

Periodic current forcing was used to investigate the intrinsic dynamics of a small group of electrically coupled neurons in the pyloric central pattern generator (CPG) of the lobster. This group contains three neurons, namely the two pyloric dilator (PD) motoneurons and the anterior burster (AB) interneuron. Intracellular current injection, using sinusoidal waveforms of varying amplitude and frequency, was applied in three configurations of the pacemaker neurons: 1) the complete pacemaker group, 2) the two PDs without the AB, and 3) the AB neuron isolated from the PDs. Depending on the frequency and amplitude of the injected current, the intact pacemaker group exhibited a wide variety of nonlinear behaviors, including synchronization to the forcing, quasiperiodicity, and complex dynamics. In contrast, a single, broad 1:1 entrainment zone characterized the response of the PD neurons when isolated from the main pacemaker neuron AB. The isolated AB responded to periodic forcing in a manner similar to the complete pacemaker group, but with wider zones of synchronization. We have built an analog electronic circuit as an implementation of a modified Hindmarsh-Rose model for simulating the membrane potential activity of pyloric neurons. We subjected this electronic model neuron to the same periodic forcing as used in the biological experiments. This four-dimensional electronic model neuron reproduced the autonomous oscillatory firing patterns of biological pyloric pacemaker neurons, and it expressed the same stationary nonlinear responses to periodic forcing as its biological counterparts. This adds to our confidence in the model. These results strongly support the idea that the intact pyloric pacemaker group acts as a uniform low-dimensional deterministic nonlinear oscillator, and the regular pyloric oscillation is the outcome of cooperative behavior of strongly coupled neurons, having different dynamical and biophysical properties when isolated.

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