Existence and Stability Criteria for Phase-Locked Modes in Ring Networks Using Phase-Resetting Curves and Spike Time Resetting Curves

2011 ◽  
pp. 419-451 ◽  
Author(s):  
Sorinel Adrian Oprisan
Keyword(s):  
Spike Time ◽  
Phase Resetting ◽  
Ring Networks ◽  
Stability Criteria ◽  
Existence And Stability ◽  
Phase Resetting Curves

Impulsive state feedback control during the sulphitation reaction in process of manufacture of sugar

2020 ◽  
pp. 2050076
Author(s):  
Guoping Pang ◽  
Xianbo Sun ◽  
Zhiqing Liang ◽  
Silian He ◽  
Xiaping Zeng
Keyword(s):  
Periodic Solution ◽  
Feedback Control ◽  
Limit Cycles ◽  
Switched Systems ◽  
State Feedback ◽  
State Feedback Control ◽  
Continuous Systems ◽  
Stability Criteria ◽  
Impulsive State Feedback Control ◽  
Existence And Stability

In this paper, the system with impulsive state feedback control corresponding to the sulphitation reaction in process of manufacture of sugar is considered. By means of square approximation and a series of switched systems, the periodic solution is approximated by a series of continuous hybrid limit cycles. Similar to the analysis of limit cycles of continuous systems, the existence and stability criteria of the order-1 periodic solution are obtained. Further, numerical analysis and discussion are given.

Predicting the Existence and Stability of Phase-Locked Mode in Neural Networks Using Generalized Phase-Resetting Curve

2017 ◽  
Vol 29 (8) ◽  
pp. 2030-2054
Author(s):  
Sorinel A. Oprisan
Keyword(s):  
Feedback Loop ◽  
Relative Phase ◽  
Open Loop ◽  
Phase Resetting ◽  
Dynamic Feedback ◽  
Neuron Network ◽  
Biologically Relevant ◽  
Existence And Stability ◽  
The Stability ◽  
Fully Connected

We used the phase-resetting method to study a biologically relevant three-neuron network in which one neuron receives multiple inputs per cycle. For this purpose, we first generalized the concept of phase resetting to accommodate multiple inputs per cycle. We explicitly showed how analytical conditions for the existence and the stability of phase-locked modes are derived. In particular, we solved newly derived recursive maps using as an example a biologically relevant driving-driven neural network with a dynamic feedback loop. We applied the generalized phase-resetting definition to predict the relative-phase and the stability of a phase-locked mode in open loop setup. We also compared the predicted phase-locked mode against numerical simulations of the fully connected network.

An Imprecise Eco-Epidemic Model with Pesticide in Relevance to Agricultural Pest Control

2018 ◽  
Vol 13 (03) ◽  
pp. 109-131
Author(s):  
Anjana Das ◽  
M. Pal
Keyword(s):  
Pest Control ◽  
Dynamical Behavior ◽  
Predator Population ◽  
Agricultural Pest ◽  
Stability Criteria ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Proposed Model ◽  
Existence And Stability ◽  
Imprecise Parameters

In this paper, we have proposed and analyzed an agricultural pest control system. For this purpose, an eco-epidemiological type predator–prey model has been proposed with the consideration of a sound predator population and two classes of pest populations namely susceptible pest and infected pest. Further to consider uncertainty, we modify our model and transform it into a fuzzy system with incorporation of imprecise parameters. The dynamical behavior of the proposed model has been investigated by examining the existence and stability criteria of all feasible equilibria. An optimal control problem is formed by considering the pesticide control as the control parameter and then the problem is solved both theoretically and numerically with the help of some computer simulation works.

Macroscopic phase-resetting curves for spiking neural networks

2017 ◽  
Vol 96 (4) ◽  
Author(s):  
Grégory Dumont ◽  
G. Bard Ermentrout ◽  
Boris Gutkin
Keyword(s):  
Neural Networks ◽  
Spiking Neural Networks ◽  
Phase Resetting ◽  
Phase Resetting Curves

scholarly journals Why are all phase resetting curves bimodal?

2013 ◽  
Vol 14 (S1) ◽  
Author(s):  
Sorinel A Oprisan ◽  
Davy Vanderweyen ◽  
Patrick Lynn ◽  
Derek Russell Tuck
Keyword(s):  
Phase Resetting ◽  
Phase Resetting Curves

scholarly journals All Phase Resetting Curves Are Bimodal, but Some Are More Bimodal Than Others

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Sorinel A. Oprisan
Keyword(s):  
Hopf Bifurcation ◽  
Oscillatory Behavior ◽  
Positive Phase ◽  
Neural Oscillator ◽  
Phase Resetting ◽  
Invariant Circle ◽  
Neural Oscillators ◽  
External Stimuli ◽  
Firing Period ◽  
Phase Resetting Curves

Phase resetting curves (PRCs) are phenomenological and quantitative tools that tabulate the transient changes in the firing period of endogenous neural oscillators as a result of external stimuli, for example, presynaptic inputs. A brief current perturbation can produce either a delay (positive phase resetting) or an advance (negative phase resetting) of the subsequent spike, depending on the timing of the stimulus. We showed that any planar neural oscillator has two remarkable points, which we called neutral points, where brief current perturbations produce no phase resetting and where the PRC flips its sign. Since there are only two neutral points, all PRCs of planar neural oscillators are bimodal. The degree of bimodality of a PRC, that is, the ratio between the amplitudes of the delay and advance lobes of a PRC, can be smoothly adjusted when the bifurcation scenario leading to stable oscillatory behavior combines a saddle node of invariant circle (SNIC) and an Andronov-Hopf bifurcation (HB).

Novel Existence and Stability Criteria of Periodic Solutions for Impulsive Delayed Neural Networks Via Coefficient Integral Averages

2016 ◽  
Vol 216 ◽  
pp. 587-595 ◽  
Author(s):  
Huamin Wang ◽  
Shukai Duan ◽  
Tingwen Huang ◽  
Chuandong Li ◽  
Lidan Wang
Keyword(s):  
Neural Networks ◽  
Periodic Solutions ◽  
Stability Criteria ◽  
Delayed Neural Networks ◽  
Existence And Stability
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