A Route to Chaotic Behavior of Single Neuron Exposed to External Electromagnetic Radiation

Abstract

Non-linear behaviors of a single neuron described by Fitzhugh-Nagumo (FHN) neuron model, with external electromagnetic radiation considered, is investigated. It is discovered that with external electromagnetic radiation in form of a cosine function, the mode selection of membrane potential occurs among periodic, quasi-periodic, and chaotic motions as increasing the frequency of external transmembrane current, which is selected as a sinusoidal function. When the frequency is small or large enough, periodic, and quasi-periodic motions are captured alternatively. Otherwise, when frequency is in interval 0.778 < ω < 2.208, chaotic motion characterizes the main behavior type. The mechanism of mode transition from quasi-periodic to chaotic motion is also observed when varying the amplitude of external electromagnetic radiation. The frequency apparently plays a more important role in determining the system behavior.

Spontaneous electromagnetic induction promotes the formation of economical neuronal network structure via self-organization process

“…The transmembrane transport of ions in neurons inevitably induces a temporally variable electromagnetic field 75,83 , which conversely exerts negative feedback on the neuronal electric activities 34,45 . A memristor model can be used to describe the physical correspondence between magnetic flux and electric charge and has recently been introduced to describe the coupling between a magnetic field and the membrane potential of a neuron 34,43,69 . The feedback current induced by the magnetic field on the membrane potential is described as 34,69 :where the negative sign reflects the inhibitory effect of the magnetic field on the neuronal membrane potential and k 1 represents the feedback strength.…”

“…However, the neuronal electric activities generated by the transmembrane flow of ions not only modulate the synaptic connection but also inevitably produce a time-varying electric field as well as a magnetic field, according to Maxwell’s theory of electromagnetic induction 34–36 . This spontaneous magnetic field around neurons may be the foundation of brain transferring sensory stimulus via complex electromagnetic flows to the cortex 37 and has significant effects on the dynamical properties of neurons and neuronal networks 34,38–41 ; for example, it induces multiple firing modes of neurons 42,43 , promotes the double coherence resonance, inhibits the stochastic resonance 40 and modulates spatiotemporal patterns 44 . Meanwhile, magnetic field interactions between neurons support a potential spatial channel for neural information transmission 45,46 and can significantly modulate signal communications between neurons 45,47 , induce firing synchronization 48,49 , trigger complex mode transitions of electrical activities 50–53 , and even offset the effect of a blocked potassium ion channel on the collective dynamics 54 .…”

Turing instability mechanism of short-memory formation in multilayer FitzHugh-Nagumo network

“…Feng et al studied the influence of external electromagnetic radiation on the FHN model. And they found that periodic, quasi-periodic, and chaotic motions would occur in different frequency intervals when the external electromagnetic radiation was in the form of a cosine function ( 12 ).…”

Toward New Modalities in VEP-Based BCI Applications Using Dynamical Stimuli: Introducing Quasi-Periodic and Chaotic VEP-Based BCI

“…Biological systems also exhibit these dynamical behaviors ( Attinger et al, 1966 ; Petrov et al, 1997 ; Suzuki et al, 2016 ) including non-oscillatory chaotic behavior, which is more complex than quasi-periodic oscillation ( Camazine et al, 2003 ; Saha and Galic, 2018 ; Strogatz, 2018 ). Neuronal systems exhibit both complex oscillatory behavior ( Llinás, 1988 ; Zhanabaev and Kozhagulov, 2013 ; Zhanabaev et al, 2016 ; Feng et al, 2017 ) as well as the non-oscillatory chaotic behavior that is seen in neurons ( Aihara et al, 1984 ; Hong, 2011 ; Lv et al, 2016 ; Ma and Tang, 2017 ) and networks ( Aihara, 1989 ; Freeman, 1992 ; Potapov and Ali, 2000 ; Rössert et al, 2015 ; Nobukawa and Nishimura, 2016 ) due to various underlying mechanisms ( Hoebeek et al, 2010 ; Ishikawa et al, 2015 ). Stimuli with dynamical patterns such as chaotic behaviors are thus expected to be more in harmony with the visual system.…”