Spiking and bursting patterns of fractional-order Izhikevich model

Teka, Wondimu; Upadhyay, Ranjit Kumar; Mondal, Argha

doi:10.1016/j.cnsns.2017.07.026

Cited by 56 publications

(36 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Diverse spiking oscillations and bursting phenomena of electrical activity in single neurons or neuronal networks play an important role in information processing and transmission across different brain areas (Connors and Gutnick, 1990;Izhikevich, 2003Izhikevich, , 2004Izhikevich, , 2007Coombes and Bressloff, 2005;Antonopoulos et al, 2015Antonopoulos et al, , 2019Ma and Tang, 2017;Mondal and Upadhyay, 2018;Teka et al, 2018). The underlying mechanism of signal processing in neurons depends on the variations of membrane voltages called spikes (Izhikevich, 2003(Izhikevich, , 2004(Izhikevich, , 2007.…”

Section: Introductionmentioning

confidence: 99%

Emergence of Mixed Mode Oscillations in Random Networks of Diverse Excitable Neurons: The Role of Neighbors and Electrical Coupling

Ghosh

Mondal

et al. 2020

Front. Comput. Neurosci.

Self Cite

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 99%

Emergence of Mixed Mode Oscillations in Random Networks of Diverse Excitable Neurons: The Role of Neighbors and Electrical Coupling

Ghosh

Mondal

et al. 2020

Front. Comput. Neurosci.

Self Cite

View full text Add to dashboard Cite

“…When mathematical models are described as a single neuron or network, then the nonlinear dynamical techniques are applied to study the emerging oscillatory patterns and the synchronization phenomena. The classical order dynamical models depend on the immediate previous response, however the fractional-order derivative depends on all the previous responses, so it has a memory effect 9–11 . It can produce a different kinds of multiple time scale neuronal dynamics 12 .…”

Section: Introductionmentioning

confidence: 99%

Firing activities of a fractional-order FitzHugh-Rinzel bursting neuron model and its coupled dynamics

Mondal

Sharma

Upadhyay

et al. 2019

Sci Rep

Self Cite

View full text Add to dashboard Cite

Fractional-order dynamics of excitable systems can be physically described as a memory dependent phenomenon. It can produce diverse and fascinating oscillatory patterns for certain types of neuron models. To address these characteristics, we consider a nonlinear fast-slow FitzHugh-Rinzel (FH-R) model that exhibits elliptic bursting at a fixed set of parameters with a constant input current. The generalization of this classical order model provides a wide range of neuronal responses (regular spiking, fast-spiking, bursting, mixed-mode oscillations, etc.) in understanding the single neuron dynamics. So far, it is not completely understood to what extent the fractional-order dynamics may redesign the firing properties of excitable systems. We investigate how the classical order system changes its complex dynamics and how the bursting changes to different oscillations with stability and bifurcation analysis depending on the fractional exponent (0 < α ≤ 1). This occurs due to the memory trace of the fractional-order dynamics. The firing frequency of the fractional-order FH-R model is less than the classical order model, although the first spike latency exists there. Further, we investigate the responses of coupled FH-R neurons with small coupling strengths that synchronize at specific fractional-orders. The interesting dynamical characteristics suggest various neurocomputational features that can be induced in this fractional-order system which enriches the functional neuronal mechanisms.

show abstract

“…Thus, the dynamical nature of fractional-order differential systems has attracted much attention and excellent results have been achieved. We refer the readers to [22][23][24][25][26][27][28]. In particular, some achievements about Hopf bifurcation of fractional-order differential systems are also available.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation of a Fractional-Order Delayed Malware Propagation Model in Social Networks

Liao

2019

Discrete Dynamics in Nature and Society

View full text Add to dashboard Cite

In recent years, with the rapid development of the Internet and the Internet of Things, network security is urgently needed. Malware becomes a major threat to network security. Thus, the study on malware propagation model plays an important role in network security. In the past few decades, numerous researchers put up various kinds of malware propagation models to analyze the dynamic interaction. However, many works are only concerned with the integer-order malware propagation models, while the investigation on fractional-order ones is very few. In this paper, based on the earlier works, we will put up a new fractional-order delayed malware propagation model. Letting the delay be bifurcation parameter and analyzing the corresponding characteristic equations of considered system, we will establish a set of new sufficient conditions to guarantee the stability and the existence of Hopf bifurcation of fractional-order delayed malware propagation model. The study shows that the delay and the fractional order have important effect on the stability and Hopf bifurcation of considered system. To check the correctness of theoretical analyses, we carry out some computer simulations. At last, a simple conclusion is drawn. The derived results of this paper are completely innovative and play an important guiding role in network security.

show abstract

Spiking and bursting patterns of fractional-order Izhikevich model

Cited by 56 publications

References 47 publications

Emergence of Mixed Mode Oscillations in Random Networks of Diverse Excitable Neurons: The Role of Neighbors and Electrical Coupling

Emergence of Mixed Mode Oscillations in Random Networks of Diverse Excitable Neurons: The Role of Neighbors and Electrical Coupling

Firing activities of a fractional-order FitzHugh-Rinzel bursting neuron model and its coupled dynamics

Bifurcation of a Fractional-Order Delayed Malware Propagation Model in Social Networks

Contact Info

Product

Resources

About