scholarly journals Complexity Induced by External Stimulations in a Neural Network System with Time Delay

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Bin Zhen ◽  
Dingyi Zhang ◽  
Zigen Song
Keyword(s):  
Time Delay ◽  
Low Frequency ◽  
Neural System ◽  
Dynamical Analysis ◽  
Quiescent State ◽  
Periodic Activity ◽  
External Stimulation ◽  
Subthreshold Oscillation ◽  
Living Organisms ◽  
Number Of Equilibria

Complexity and dynamical analysis in neural systems play an important role in the application of optimization problem and associative memory. In this paper, we establish a delayed neural system with external stimulations. The complex dynamical behaviors induced by external simulations are investigated employing theoretical analysis and numerical simulation. Firstly, we illustrate number of equilibria by the saddle-node bifurcation of nontrivial equilibria. It implies that the neural system has one/three equilibria for the external stimulation. Then, analyzing characteristic equation to find Hopf bifurcation, we obtain the equilibrium’s stability and illustrate periodic activity induced by the external stimulations and time delay. The neural system exhibits a periodic activity with the increased delay. Further, the external stimulations can induce and suppress the periodic activity. The system dynamics can be transformed from quiescent state (i.e., the stable equilibrium) to periodic activity and then quiescent state with stimulation increasing. Finally, inspired by ubiquitous rhythm in living organisms, we introduce periodic stimulations with low frequency as rhythm activity from sensory organs and other regions. The neural system subjected by the periodic stimulations exhibits some interesting activities, such as periodic spiking, subthreshold oscillation, and bursting-like activity. Moreover, the subthreshold oscillation can switch its position with delay increasing. The neural system may employ time delay to realize Winner-Take-All functionality.

scholarly journals Dynamical analysis of a giving up smoking model with time delay

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Zizhen Zhang ◽  
Ruibin Wei ◽  
Wanjun Xia
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Local Stability ◽  
Center Manifold ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Dynamical Analysis ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Form Theory

AbstractIn this paper, we are concerned with a delayed smoking model in which the population is divided into five classes. Sufficient conditions guaranteeing the local stability and existence of Hopf bifurcation for the model are established by taking the time delay as a bifurcation parameter and employing the Routh–Hurwitz criteria. Furthermore, direction and stability of the Hopf bifurcation are investigated by applying the center manifold theorem and normal form theory. Finally, computer simulations are implemented to support the analytic results and to analyze the effects of some parameters on the dynamical behavior of the model.

Dynamical behavior of simplified FitzHugh–Nagumo neural system with time delay driven by Lévy noise

2021 ◽  
pp. 2150240
Author(s):  
Weida Qiu ◽  
Yongfeng Guo ◽  
Xiuxian Yu
Keyword(s):  
Time Delay ◽  
First Passage Time ◽  
Dynamical Behavior ◽  
Passage Time ◽  
Neural System ◽  
The Other ◽  
Lévy Noise ◽  
First Passage ◽  
Levy Noise ◽  
System With Time Delay

In this paper, the dynamical behavior of the FitzHugh–Nagumo (FHN) neural system with time delay driven by Lévy noise is studied from two aspects: the mean first-passage time (MFPT) and the probability density function (PDF) of the first-passage time (FPT). Using the Janicki–Weron algorithm to generate the Lévy noise, and through the order-4 Runge–Kutta algorithm to simulate the FHN system response, the time that the system needs from one stable state to the other one is tracked in the process. Using the MATLAB software to simulate the process above 20,000 times and recording the PFTs, the PDF of the FPT and the MFPT is obtained. Finally, the effects of the Lévy noise and time-delay on the FPT are discussed. It is found that the increase of both time-delay feedback intensity and Lévy noise intensity can promote the transition of the particle from the resting state to the excited state. However, the two parameters produce the opposite effects in the other direction.

Two bifurcation routes to multiple chaotic coexistence in an inertial two-neural system with time delay

2018 ◽  
Vol 95 (2) ◽  
pp. 1549-1563 ◽  
Author(s):  
Shengwei Yao ◽  
Liwang Ding ◽  
Zigen Song ◽  
Jieqiong Xu
Keyword(s):  
Time Delay ◽  
Neural System ◽  
System With Time Delay

scholarly journals BeiDa Imaging Electron Spectrometer observation of multi-period electron flux modulation caused by localized ultra-low-frequency waves

2020 ◽  
Vol 38 (4) ◽  
pp. 801-813
Author(s):  
Xingran Chen ◽  
Qiugang Zong ◽  
Hong Zou ◽  
Xuzhi Zhou ◽  
Li Li ◽  
...  
Keyword(s):  
Time Delay ◽  
Electron Flux ◽  
Particle Interaction ◽  
Energetic Electron ◽  
Low Frequency ◽  
Particle Energy ◽  
Energy Change ◽  
Electron Spectrometer ◽  
Resonance Theory ◽  
Energy Channels

Abstract. We present multi-period modulation of energetic electron flux observed by the BeiDa Imaging Electron Spectrometer (BD-IES) on board a Chinese navigation satellite on 13 October 2015. Electron flux oscillations were observed at a dominant period of ∼190 s in consecutive energy channels from ∼50 to ∼200 keV. Interestingly, flux modulations at a secondary period of ∼400 s were also unambiguously observed. The oscillating signals at different energy channels were observed in sequence, with a time delay of up to ∼900 s. This time delay far exceeds the oscillating periods, by which we speculate that the modulations were caused by localized ultra-low-frequency (ULF) waves. To verify the wave–particle interaction scenario, we revisit the classic drift-resonance theory. We adopt the calculation method therein to derive the electron energy change in a multi-period ULF wave field. Then, based on the modeled energy change, we construct the flux variations to be observed by a virtual spacecraft. The predicted particle signatures well agree with the BD-IES observations. We demonstrate that the particle energy change might be underestimated in the conventional theories, as the Betatron acceleration induced by the curl of the wave electric field was often omitted. In addition, we show that azimuthally localized waves would notably extend the energy width of the resonance peak, whereas the drift-resonance interaction is only efficient for particles at the resonant energy in the original theory.

scholarly journals Use of biophysical methods to improve yields and quality of agricultural products

2008 ◽  
Vol 53 (3) ◽  
pp. 235-242 ◽  
Author(s):  
Branko Marinkovic ◽  
Miroslav Grujic ◽  
Dusko Marinkovic ◽  
Jovan Crnobarac ◽  
Jelena Marinkovic ◽  
...  
Keyword(s):  
Radiation Effects ◽  
Biological Systems ◽  
Low Frequency ◽  
Crop Species ◽  
Human Environment ◽  
Electromagnetic Stimulation ◽  
Stimulation Method ◽  
Living Organisms ◽  
Novi Sad ◽  
The University

Until as recently as a century ago, the exposure of biological systems to radiation was limited only to the natural sources. Today, however, a broad range of radiation types and doses have found a wide variety of uses and applications, so much so that it would be difficult to make a list of all the areas of human activity in which radiation is used for one purpose or another. The study of radiation effects on individuals and populations as a whole has become important only with the development of methods and sources of man-made radiation. Given that what is present in this case are physical effects on biological systems (living organisms), all these methods can be placed under the heading of biophysical influences. In the last 50 years, the effects of extremely low-frequency electromagnetic fields (ELF-EMF) have been studied with great diligence. These fields are the ones most commonly found in the human environment and they have been used in our studies in this field. The present paper provides a brief review of the literature data and our findings on the effects of ELF-EMF on various crop species using the RIES (Resonant Impulse Electromagnetic Stimulation) method, developed at the Faculty of Agriculture of the University of Novi Sad.

scholarly journals A quiescent state following mild sensory arousal in Caenorhabditis elegans is potentiated by stress

2019 ◽  
Author(s):  
Patrick D. McClanahan ◽  
Jessica M. Dubuque ◽  
Daphne Kontogiorgos-Heintz ◽  
Ben F. Habermeyer ◽  
Joyce H. Xu ◽  
...  
Keyword(s):  
Caenorhabditis Elegans ◽  
Light Exposure ◽  
Light Stimulus ◽  
Low Frequency ◽  
Behavioral Responses ◽  
Quiescent State ◽  
Sleep State ◽  
C Elegans ◽  
Epidermal Growth ◽  
Cellular Stressors

AbstractAn animal’s behavioral and physiological response to stressors includes changes to its responses to stimuli. How such changes occur is not well understood. Here we describe a Caenorhabditis elegans quiescent behavior, post-response quiescence (PRQ), which is modulated by the C. elegans response to cellular stressors. Following an aversive mechanical or blue light stimulus, worms respond first by briefly moving, and then become more quiescent for a period lasting tens of seconds. PRQ occurs at low frequency in unstressed animals, but is more frequent in animals that have experienced cellular stress due to ultraviolet light exposure as well as in animals following overexpression of epidermal growth factor (EGF). PRQ requires the function of the carboxypeptidase EGL-21 and the calcium-activated protein for secretion (CAPS) UNC-31, suggesting it has a neuropeptidergic mechanism. Although PRQ requires the sleep-promoting neurons RIS and ALA, it is not accompanied by decreased arousability, and does not appear to be homeostatically regulated, suggesting that it is not a sleep state. PRQ represents a simple, tractable model for studying how neuromodulatory states like stress alter behavioral responses to stimuli.

scholarly journals Sequences of Intonation Units form a ~ 1 Hz rhythm

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Maya Inbar ◽  
Eitan Grossman ◽  
Ayelet N. Landau
Keyword(s):  
Speech Processing ◽  
Temporal Structure ◽  
Low Frequency ◽  
Neural System ◽  
Specific Pattern ◽  
Physiological Data ◽  
Low Frequencies ◽  
Speech Stimuli ◽  
Intonation Units ◽  
Speech Envelope

Abstract Studies of speech processing investigate the relationship between temporal structure in speech stimuli and neural activity. Despite clear evidence that the brain tracks speech at low frequencies (~ 1 Hz), it is not well understood what linguistic information gives rise to this rhythm. In this study, we harness linguistic theory to draw attention to Intonation Units (IUs), a fundamental prosodic unit of human language, and characterize their temporal structure as captured in the speech envelope, an acoustic representation relevant to the neural processing of speech. IUs are defined by a specific pattern of syllable delivery, together with resets in pitch and articulatory force. Linguistic studies of spontaneous speech indicate that this prosodic segmentation paces new information in language use across diverse languages. Therefore, IUs provide a universal structural cue for the cognitive dynamics of speech production and comprehension. We study the relation between IUs and periodicities in the speech envelope, applying methods from investigations of neural synchronization. Our sample includes recordings from every-day speech contexts of over 100 speakers and six languages. We find that sequences of IUs form a consistent low-frequency rhythm and constitute a significant periodic cue within the speech envelope. Our findings allow to predict that IUs are utilized by the neural system when tracking speech. The methods we introduce here facilitate testing this prediction in the future (i.e., with physiological data).

scholarly journals Influence of Time Delay in Signal Transmission on Synchronization between Two Coupled FitzHugh-Nagumo Neurons

2019 ◽  
Vol 9 (10) ◽  
pp. 2159 ◽  
Author(s):  
Bin Zhen ◽  
Zhenhua Li ◽  
Zigen Song
Keyword(s):  
Time Delay ◽  
Energy Method ◽  
Signal Transmission ◽  
Coupled System ◽  
Original System ◽  
Neural System ◽  
Periodic Part ◽  
Change Rate ◽  
Error System ◽  
Synchronization Problems

In this paper, the energy method is employed to analytically investigate the influence of time delay in signal transmission on synchronization between two coupled FitzHugh-Nagumo (FHN) neurons. Unlike pre-existing methods that deal with synchronization problems, our major idea is to consider the change rate of the energy of the synchronization error system, since the original system’s synchronization is equivalent to the disappearance of the energy of the error system. In rewriting the original coupled system in the corresponding energy coordinates based on the energy method, we find that the change rate of energy of the error system can be divided into two parts (periodic and non-periodic). The synchronization criterion for the original system can then be obtained by letting the non-periodic part of the change rate of the energy be less than zero. The correctness of the analysis is illustrated with numerical simulations. Our analytical results show that time delay in signal transmission has very significant effects on the synchronization between two FHN neurons. If the time delay in signal transmission is not taken into account in the two coupled FHN neurons, synchronous spikes cannot be achieved in the system for any given coupling strength. By adjusting the value of the time delay in signal transmission, the neural system can freely switch between neural rest and synchronous spikes. This means that time delay in signal transmission is crucial for the occurrence of synchronous spikes in the FHN neural system, which contributes to our understanding of the interaction between neurons. We analytically show the influence of the time delay on the synchronization between two FHN neurons, which was seldom considered by other researchers.

Sign in / Sign up

Export Citation Format

Share Document