Bifurcations of Negative Responses to Positive Feedback Current Mediated by Memristor in a Neuron Model with Bursting Patterns

2020 ◽  
Vol 30 (04) ◽  
pp. 2030009 ◽  
Author(s):  
Fuqiang Wu ◽  
Huaguang Gu

In contrast to traditional viewpoint that positive feedback current always enhances neural firing activities, in the present paper, we identify that the excitatory feedback current mediated by memristor can induce negative responses of bursting patterns, which can be well interpreted with bifurcations. For the Hindmarsh–Rose neuron model without memristor, the period-adding bifurcations of bursting patterns and increase of firing frequency can be induced by increasing the excitatory effect of the background current. After introducing a memristor to simulate the biological synapse or electromagnetic induction effect, inverse period-adding or complex bifurcations of bursting patterns are induced by the excitatory feedback current mediated by the memristor. The number of spikes per burst becomes smaller and the firing frequency becomes lower when increasing the positive feedback gain. Such negative responses of bursting patterns to the positive feedback current are demonstrated in a circuit designed with Digital Signal Processor systems of the MatLab software. Furthermore, the underlying bifurcation mechanism of the negative responses to the positive feedback is acquired with fast–slow variable dissection method. With increasing feedback gain, the initial phase of the burst, which corresponds to a saddle-node bifurcation point of the fast subsystem, delays, while the termination phase of the burst, which corresponds to a saddle-homoclinic bifurcation point, remains unchanged. Therefore, the burst becomes narrower with increasing feedback gain, which leads to decrease in the number of spikes within a burst and decrease in firing frequency. The results present a paradoxical nonlinear phenomenon and the dynamical mechanism, which is helpful for understanding the functions of memristor and roles of the electromagnetic induction current.

2022 ◽  
Author(s):  
Li Li ◽  
Zhiguo Zhao ◽  
Huaguang Gu

Abstract Post-inhibitory rebound (PIR) spike, which has been widely observed in diverse nervous systems with different physiological functions and simulated in theoretical models with class 2 excitability, presents a counterintuitive nonlinear phenomenon in that the inhibitory effect can facilitate neural firing behavior. In this study, a PIR spike induced by inhibitory stimulation from the resting state corresponding to class 3 excitability that is not related to bifurcation is simulated in the Morris-Lecar neuron. Additionally, the inhibitory self-feedback mediated by an autapse with time delay can evoke tonic/repetitive spiking from phasic/transient spiking. The dynamical mechanism for the PIR spike and the tonic/repetitive spiking is acquired with the phase plane analysis and the shape of the quasi-separatrix curve. The result extends the counterintuitive phenomenon induced by inhibition to class 3 excitability, which presents a potential function of inhibitory autapse and class 3 neuron in many neuronal systems such as the auditory system.


2021 ◽  
Author(s):  
Ante Lojic Kapetanovic ◽  
Anna Susnjara ◽  
Dragan Poljak

Abstract This paper examines the effect of electromagnetic induction on the electrophysiology of a single cortex neuronthrough two different modes associated with the nature of the external neuronal stimulus. By using the recently extended induction-based variant of the well-known and biologically plausible Hodgkin-Huxley neuron model, bifurcation analysis is performed. Electromagnetic induction caused by magnetic flux is captured using a polynomial approximation of a memristor embedded into the neuron model. In order to determine true influence of the variability of ion channels conductivity, the stochastic sensitivity analysis is performed post hoc. Additionally, numerical simulations are enriched with uncertainty quantification, observing values of ion channels conductivity as random variables. The aim of the study is to computationally determine the sensitivity of the action potential dynamics with respect to the changes in conductivity of each ion channel so that the future experimental procedures, most often medical treatments, may be adapted to different individuals in various environmental conditions.


2010 ◽  
Vol 16 (3) ◽  
pp. 3-14 ◽  
Author(s):  
V.M. Kartashev ◽  
◽  
P.S. Kizim ◽  
V.E. Kovtun ◽  
S.N. Stervoiedov ◽  
...  

Author(s):  
Won-Chul Bing

The Korean Baseball Organization (KBO) League is a sports culture that Koreans love and enjoy most. However, the launch of the KBO League is related to political issues in Korea. The purpose of this study is to explain the launch history of the KBO league through a sociopolitical approach. The history of the KBO league was explained by applying a complex paradigm that explains sociocultural phenomena from a new perspective. This study used historical analysis, a qualitative study approach. Literature related to Korean professional baseball, complex system theory, sports, and politics were reviewed. This study introduces the characteristics and theory of the complex system paradigm and analyzes the history of the KBO League based on this theory. The edge of chaos, bifurcation point, positive feedback, emergence of the theory of complex system are used as elements of an overall theoretical framework to analyze the history and development of the KBO league. The study results are explained in four frameworks. First, the KBO was launched on the edge of chaos, or in the midst of social chaos provoked by Chun Doo-Hwan, who seized power through a military coup. Second, the Chun Doo-Hwan regime launched the professional baseball league to divert the public’s attention from politics to sports and provided support to construct baseball fields as venues for the national pastime. The Chun Doo-Hwan regime’s appeasement policy became a bifurcation point, which promoted the launch of the professional baseball league. Third, from the viewpoint of the complex system paradigm, the launch of the Korean baseball league was enabled by the positive feedback of the Korea professional baseball promotion committee, established in 1975 under the initiative of Korean American businessman Hong Yoon-Hee. Fourth, the Korean professional baseball league led to the emergence of the consumption culture of professional sports, and it became a national leisure and a crucial part of Korea’s sports culture. In terms of sociopolitical, the KBO League started in the dark of Korean society, but it is becoming a vitality for Korean sports culture and health.


2018 ◽  
Vol 32 (30) ◽  
pp. 1850332 ◽  
Author(s):  
Xiaoqiang Liu ◽  
Xiaoli Yang

The influences of phase noise together with autapse on the resonance dynamics in a modified FitzHugh–Nagumo (FHN) neuron are investigated by numerical simulation, where the neuronal model is in the environment of electromagnetic induction. First, it is found that phase noise can induce double coherence resonances, which is further confirmed to be robust to the feedback gain of induction current. Surprisingly, by individually changing the period of phase noise and the feedback gain, a resonance-like behavior also appears. Subsequently, the significant phenomenon of autapse-induced multiple coherence resonances is discovered. Moreover, the phenomenon of multiple coherence resonances can emerge at a broad parameter range of autaptic strength and autaptic delay.


Author(s):  
Cassius R. Aguiar ◽  
Amilcar F. Q. Goncalves ◽  
Renan F. Bastos ◽  
Giovani G. Pozzebon ◽  
Jose R. B. A. Monteiro ◽  
...  

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Zhongquan Gao ◽  
Zhixuan Yuan ◽  
Zuo Wang ◽  
Peihua Feng

Both of astrocytes and electromagnetic induction are magnificent to modulate neuron firing by introducing feedback currents to membrane potential. An improved astro-neuron model considering both of the two factors is employed to investigate their different roles in modulation. The mixing mode, defined by combination of period bursting and depolarization blockage, characterizes the effect of astrocytes. Mixing mode and period bursting alternatively appear in parameter space with respect to the amplitude of feedback current on neuron from astrocyte modulation. However, magnetic flux obviously plays a role of neuron firing inhibition. It not only repels the mixing mode but also suppresses period bursting. The mixing mode becomes period bursting mode and even resting state when astrocytes are hyperexcitable. Abnormal activities of astrocytes are capable to induce depolarization blockage to compose the mixing mode together with bursting mode. But electromagnetic induction shows its strong ability of inhibition of neuron firing, which is also illustrated in the bifurcation diagram. Indeed, the combination of the two factors and appropriate choice of parameters show the great potential to control disorder of neuron firing like epilepsy.


Author(s):  
L. Mahadevan ◽  
J. M. Deutch

We consider the dynamical evolution of a simple climate system that describes the average temperature of the Earth’s atmosphere owing to radiative forcing and coupling to a positive feedback variable such as the concentration of greenhouse gases in the presence of fluctuations. Analysing the resulting stochastic dynamical system shows that, if the temperature relaxes rapidly relative to the concentration, the time-dependent and stationary probability density functions (pdfs) for the temperature rise possess a fat tail. In contrast, if the feedback variable relaxes rapidly relative to the temperature, the pdf has no fat tail, and, instead, the system shows critical slowing down as the singular limit of positive feedback is approached. However, if there is uncertainty in the feedback variable itself, a fat tail can reappear. Our analysis may be generalized to more complex models with similar qualitative results. Our results have policy implications: although fat tails imply that the expectation of plausible damage functions is infinite, the pdfs permit an examination of the trade-off between reducing emissions and reducing the positive feedback gain.


2011 ◽  
Vol 25 (29) ◽  
pp. 3977-3986 ◽  
Author(s):  
HUAGUANG GU ◽  
HUIMIN ZHANG ◽  
CHUNLING WEI ◽  
MINGHAO YANG ◽  
ZHIQIANG LIU ◽  
...  

Coherence resonance at a saddle-node bifurcation point and the corresponding stochastic firing patterns are simulated in a theoretical neuronal model. The characteristics of noise-induced neural firing pattern, such as exponential decay in histogram of interspike interval (ISI) series, independence and stochasticity within ISI series are identified. Firing pattern similar to the simulated results was discovered in biological experiment on a neural pacemaker. The difference between this firing and integer multiple firing generated at a Hopf bifurcation point is also given. The results not only revealed the stochastic dynamics near a saddle-node bifurcation, but also gave practical approaches to identify the saddle-node bifurcation and to distinguish it from the Hopf bifurcation in neuronal system. In addition, many previously observed firing patterns can be attribute to stochastic firing pattern near such a saddle-node bifurcation.


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