Bursting Oscillations in Two Coupled FitzHugh-Nagumo Systems

Complexus ◽  
2003 ◽  
Vol 1 (3) ◽  
pp. 101-111 ◽  
Author(s):  
Catherine Doss-Bachelet ◽  
Jean-Pierre Françoise ◽  
Claude Piquet
Keyword(s):  
Bursting Oscillations

Bursting Oscillations and Experimental Verification of a Rucklidge System

2021 ◽  
Vol 31 (08) ◽  
pp. 2130023
Author(s):  
Zhijun Li ◽  
Siyuan Fang ◽  
Minglin Ma ◽  
Mengjiao Wang
Keyword(s):  
Electronic Devices ◽  
Pitchfork Bifurcation ◽  
Phase Portraits ◽  
Formation Mechanisms ◽  
Analysis Method ◽  
Good Qualitative Agreement ◽  
Bursting Oscillations ◽  
Real Time Measurement ◽  
Time Varying Parameter ◽  
Measurement Results

Bursting oscillations are ubiquitous in multi-time scale systems and have attracted widespread attention in recent years. However, research on experimental demonstration of the bursting oscillations induced by delayed bifurcation is very rarely reported. In this paper, a parametrically driven Rucklidge system is introduced and a distinct delayed behavior is observed when the time-varying parameter passes through the pitchfork bifurcation point. Different bursting patterns induced by such a delayed behavior are numerically investigated under different excitation amplitudes based on the fast–slow analysis method. Furthermore, in order to reproduce the bursting electronic signals and explore the underlying formation mechanisms experimentally, a real physical circuit of the parametrically driven Rucklidge system is developed by using off-the-shelf electronic devices. The real-time measurement results such as time series, phase portraits and transformed phase portraits are in good qualitative agreement with those obtained from the numerical computations. The experimental evidence to verify bursting oscillations induced by delayed pitchfork bifurcation is thus provided in this study.

scholarly journals Bursting Oscillations and Sliding Motion in Permanent Magnet Synchronous Motor Systems with Friction Factor

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Rui Qu ◽  
Shaolong Li
Keyword(s):  
Permanent Magnet ◽  
Friction Factor ◽  
Permanent Magnet Synchronous Motor ◽  
Synchronous Motor ◽  
Governing Equations ◽  
Bursting Oscillations ◽  
Sliding Motion ◽  
Friction Function ◽  
Filippov Type ◽  
Theoretical Results

The main purpose of this paper is to investigate the qualitative effects of external excitation and friction factor on the response of permanent magnet synchronous motor (PMSM) system. Three different modes of bursting oscillations are found. In particular, the introduction of friction function changes the governing equations from a smooth type to a nonsmooth (Filippov) type in which the special sliding motion is observed. The mechanism, attractor structure, vector field structure, and analytic bifurcation conditions of bursting oscillation and sliding motion are discussed in detail. The validity of theoretical results obtained is verified by numerical simulations and analysis.

scholarly journals Topological and phenomenological classification of bursting oscillations

1995 ◽  
Vol 57 (3) ◽  
pp. 413-439 ◽  
Author(s):  
Richard Bertram ◽  
Manish J. Butte ◽  
Tim Kiemel ◽  
Arthur Sherman
Keyword(s):  
Bursting Oscillations

Propagation of bursting oscillations

2009 ◽  
Vol 367 (1908) ◽  
pp. 4863-4875 ◽  
Author(s):  
Benjamin Ambrosio ◽  
Jean-Pierre Françoise
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Time Evolution ◽  
Global Attractor ◽  
Reaction Diffusion ◽  
Functional Space ◽  
Excitable Cells ◽  
Diffusion Type ◽  
Bursting Oscillations

We investigate a system of partial differential equations of reaction–diffusion type which displays propagation of bursting oscillations. This system represents the time evolution of an assembly of cells constituted by a small nucleus of bursting cells near the origin immersed in the middle of excitable cells. We show that this system displays a global attractor in an appropriated functional space. Numerical simulations show the existence in this attractor of recurrent solutions which are waves propagating from the central source. The propagation seems possible if the excitability of the neighbouring cells is above some threshold.

Bursting Oscillations as well as the Mechanism in a Filippov System with Parametric and External Excitations

2020 ◽  
Vol 30 (12) ◽  
pp. 2050168
Author(s):  
Hongfang Han ◽  
Qinsheng Bi
Keyword(s):  
Autonomous System ◽  
Type System ◽  
External Excitation ◽  
Nonsmooth Boundary ◽  
Bursting Oscillations ◽  
Fold Bifurcation ◽  
Different Types ◽  
Boundary Equilibrium ◽  
Parametric And External Excitations ◽  
Filippov Type

The main purpose of this paper is to explore the bursting oscillations as well as the mechanism of a parametric and external excitation Filippov type system (PEEFS), in which different types of bursting oscillations such as fold/nonsmooth fold (NSF)/fold/NSF, fold/NSF/fold and fold/fold bursting oscillations can be observed. By employing the overlap of the transformed phase portrait and the equilibrium branches of the generalized autonomous system, the mechanisms of the bursting oscillations are investigated. Our results show that the fold bifurcation and the boundary equilibrium bifurcation (BEB) can cause the transitions between the quiescent states and repetitive spiking states. The oscillating frequencies of the spiking states can be approximated theoretically by their occurring mechanisms, which agree well with the numerical simulations. Furthermore, some nonsmooth evolutions are investigated by employing differential inclusions theory, which reveals that the positional relationship between the points of the trajectory interacting with the nonsmooth boundary and the related sliding boundary of the nonsmooth system may affect the nonsmooth evolutions.

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