Obtaining amplitude-modulated bursting by multiple-frequency slow parametric modulation

Han, Xiujing; Wei, Mengke; Bi, Qinsheng; Kurths, Jürgen

doi:10.1103/physreve.97.012202

Cited by 30 publications

(6 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this way, a cyclic folded-node can be robust even if the torus canards are not robust. This has been proposed very recently by Vo and colleagues [ 81 , 82 ] via a specific example that links the resulting dynamics to the amplitude-modulated bursting already mentioned in [ 44 , 78 ]; see also [ 83 – 85 ] for other examples of amplitude-modulated bursting.…”

Section: Introductionmentioning

confidence: 99%

Classification of bursting patterns: A tale of two ducks

2022

View full text Add to dashboard Cite

Bursting is one of the fundamental rhythms that excitable cells can generate either in response to incoming stimuli or intrinsically. It has been a topic of intense research in computational biology for several decades. The classification of bursting oscillations in excitable systems has been the subject of active research since the early 1980s and is still ongoing. As a by-product, it establishes analytical and numerical foundations for studying complex temporal behaviors in multiple timescale models of cellular activity. In this review, we first present the seminal works of Rinzel and Izhikevich in classifying bursting patterns of excitable systems. We recall a complementary mathematical classification approach by Bertram and colleagues, and then by Golubitsky and colleagues, which, together with the Rinzel-Izhikevich proposals, provide the state-of-the-art foundations to these classifications. Beyond classical approaches, we review a recent bursting example that falls outside the previous classification systems. Generalizing this example leads us to propose an extended classification, which requires the analysis of both fast and slow subsystems of an underlying slow-fast model and allows the dissection of a larger class of bursters. Namely, we provide a general framework for bursting systems with both subthreshold and superthreshold oscillations. A new class of bursters with at least 2 slow variables is then added, which we denote folded-node bursters, to convey the idea that the bursts are initiated or annihilated via a folded-node singularity. Key to this mechanism are so-called canard or duck orbits, organizing the underpinning excitability structure. We describe the 2 main families of folded-node bursters, depending upon the phase (active/spiking or silent/nonspiking) of the bursting cycle during which folded-node dynamics occurs. We classify both families and give examples of minimal systems displaying these novel bursting patterns. Finally, we provide a biophysical example by reinterpreting a generic conductance-based episodic burster as a folded-node burster, showing that the associated framework can explain its subthreshold oscillations over a larger parameter region than the fast subsystem approach.

show abstract

Section: Introductionmentioning

confidence: 99%

Classification of bursting patterns: A tale of two ducks

2022

View full text Add to dashboard Cite

show abstract

“…In this way, a cyclic foldednode can be robust even if the torus canards are not robust. This has been proposed very recently by Vo and collaborators [55,57] via a specific example that links the resulting dynamics to the amplitude-modulated bursting already mentioned in [29,31]; see also [24] for other examples of amplitude-modulated bursting. In summary, we herein propose a taxonomy of cyclic folded-node bursting patterns, with several numerical examples, which completes our extension of the previous bursting classifications.…”

Section: Cyclic Folded-node Casementioning

confidence: 99%

Towards a new classification of bursting patterns: review & extensions

Desroches,

Rinzel,

Rodrigues

2020

Preprint

View full text Add to dashboard Cite

The mathematical classification of complex bursting oscillations in multiscale excitable systems, seen for example in physics and neuroscience, has been the subject of active enquiry since the early 1980s and is still ongoing. This classification problem is fundamental as it also establishes analytical and numerical foundations for studying complex temporal behaviours in multiple timescale models. This manuscript begins by reviewing the seminal works of Rinzel [43] and Izhikevich [27] in classifying bursting patterns of excitable cell models. Moreover, we recall an alternative, yet complementary, mathematical classification approach by Golubitsky, which together with the Rinzel-Izhikevich proposals provide the state-of-the-art foundations to the classification problem. Unexpectedly, while keeping within the Rinzel-Izhikevich framework, we find novel cases of bursting mechanisms, which were not considered before. Moving beyond the state-of-the-art, we identify novel bursting mechanisms that fall outside the Rinzel, Izhikevich and Golubitsky classification system. This leads us towards a new classification, which requires the analysis of both the fast and the slow subsystems of an underlying slow-fast model. This new classification allows the dynamical dissection of a larger class of bursters. To substantiate this, we add a new class of bursters with at least two slow variables, which we denote foldednode bursters, to convey the idea that the bursts are initiated or annihilated via a folded-node singularity. In fact, there are two main families of folded-node bursters, depending upon the phase of the bursting cycle during which folded-node dynamics occurs. If it occurs during the silent phase, we obtain the classical folded-node bursting (or simply folded-node bursting). If it occurs during the active phase, we have cyclic folded-node bursting. We classify both families and give examples of minimal systems displaying these novel types of bursting behaviour.

show abstract

“…It is noteworthy that the system exhibits complex MBCBOs. For instance, periodic, quasi-periodic and chaotic MBCBOs are uncovered, which are caused by the cascading of pitchfork bifurcation-delay-induced hysteresis (PBDIH) [20], homoclinic orbit (HO) and Hopf bifurcation (HB). Unfortunately, these complicated MBCBOs were never studied, and the mechanism of various modes of MBCBOs is not revealed in detail.…”

Section: Introductionmentioning

confidence: 99%

Multi-bifurcation cascaded bursting oscillations and mechanism in a novel 3D non-autonomous circuit system with parametric and external excitation

Wang

Zhang

et al. 2021

Nonlinear Dyn

View full text Add to dashboard Cite

In this paper, multi-timescale dynamics and the formation mechanism of a 3D non-autonomous system with two slowly varying periodic excitations are systematically investigated. Interestingly, the system shows novel multibifurcation cascaded bursting oscillations (MBCBOs) when the frequency of the two excitations is much lower than the mean frequency of the original system (MFOS). For instance, periodic, quasi-periodic and chaotic bursting oscillations induced by a variety of cascaded bifurcations are first observed, and the phenomenon of spiking transfer is also revealed. Besides, stability and local bifurcations of the system are comprehensively investigated to analyze the mechanism of the observed MBCBOs, in which bifurcation diagram, Lyapunov exponents, time series, phase portraits, and transformed phase diagrams are used. Finally, through a circuit simulation and hardware experiment, these complex dynamics phenomena are verified physically.

show abstract

Obtaining amplitude-modulated bursting by multiple-frequency slow parametric modulation

Cited by 30 publications

References 30 publications

Classification of bursting patterns: A tale of two ducks

Classification of bursting patterns: A tale of two ducks

Towards a new classification of bursting patterns: review & extensions

Multi-bifurcation cascaded bursting oscillations and mechanism in a novel 3D non-autonomous circuit system with parametric and external excitation

Contact Info

Product

Resources

About