scholarly journals Stochastic Bifurcations and Noise-Induced Chaos in 3D Neuron Model

2016 ◽  
Vol 26 (12) ◽  
pp. 1630032 ◽  
Author(s):  
Irina Bashkirtseva ◽  
Sergei Fedotov ◽  
Lev Ryashko ◽  
Evdokia Slepukhina
Keyword(s):  
Stochastic Dynamics ◽  
Stable Equilibrium ◽  
Deterministic Model ◽  
Three Dimensional ◽  
Random Disturbances ◽  
Stable Equilibria ◽  
Relationship Of ◽  
Stochastic Bifurcations ◽  
Good Agreement ◽  
Qualitative Changes

The stochastically forced three-dimensional Hindmarsh–Rose model of neural activity is considered. We study the effect of random disturbances in parametric zones where the deterministic model exhibits mono- and bistable dynamic regimes with period-adding bifurcations of oscillatory modes. It is shown that in both cases the phenomenon of noise-induced bursting is observed. In the monostable zone, where the only attractor of the system is a stable equilibrium, this effect is connected with a stochastic generation of large-amplitude oscillations due to the high excitability of the model. In a parametric zone of coexisting stable equilibria and limit cycles, bursts appear due to noise-induced transitions between the attractors. For a quantitative analysis of the noise-induced bursting and corresponding stochastic bifurcations, an approach based on the stochastic sensitivity function (SSF) technique is applied. Our estimations of the strength of noise that generates such qualitative changes in stochastic dynamics are in a good agreement with the direct numerical simulation. A relationship of the noise-induced generation of bursts with transitions from order to chaos is discussed.

scholarly journals Variability of complex oscillatory regimes in the stochastic model of cold-flame combustion of a hydrocarbon mixture

2022 ◽  
Vol 380 (2217) ◽  
Author(s):  
I. Bashkirtseva ◽  
E. Slepukhina
Keyword(s):  
Deterministic Model ◽  
Three Dimensional ◽  
Hydrocarbon Mixture ◽  
Nonlinear Dynamical ◽  
Flame Combustion ◽  
Mixed Mode Oscillations ◽  
Random Forcing ◽  
Random Disturbances ◽  
Stable Equilibria ◽  
Cold Flame

Processes of the cold-flame combustion of a mixture of two hydrocarbons are studied on the base of a three-dimensional nonlinear dynamical model. Bifurcation analysis of the deterministic model reveals mono- and bistability parameter zones with equilibrium and oscillatory attractors. For this model, effects of random disturbances in the bistability parameter zone are studied. We show that random forcing causes transitions between coexisting stable equilibria and limit cycles with the formation of complex stochastic mixed-mode oscillations. Properties of these oscillatory regimes are studied by means of statistics of interspike intervals. A phenomenon of anti-coherence resonance is discussed. This article is part of the theme issue ‘Transport phenomena in complex systems (part 2)’.

Jacobi analysis for an unusual 3D autonomous system

2020 ◽  
Vol 17 (04) ◽  
pp. 2050062 ◽  
Author(s):  
Chunsheng Feng ◽  
Qiujian Huang ◽  
Yongjian Liu
Keyword(s):  
Chaotic System ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Chen System ◽  
Parameter Region ◽  
Stable Equilibria ◽  
The Lorenz System ◽  
Deviation Vector

Little seems to be known about the study of the chaotic system with only Lyapunov stable equilibria from the perspective of differential geometry. Therefore, this paper presents Jacobi analysis of an unusual three-dimensional (3D) autonomous chaotic system. Under certain parameter conditions, this system has positive Lyapunov exponents and only two linear stable equilibrium points, which means that chaotic attractor and Lyapunov stable equilibria coexist. The dynamical behavior of the deviation vector near the whole trajectories (including all equilibrium points) is analyzed in detail. The results show that the value of the deviation curvature tensor at equilibrium points is only related to parameters; the two equilibrium points of the system are Jacobi stable if the parameters satisfy certain conditions. Particularly, for a specific set of parameters, the linear stable equilibrium points of the system are always Jacobi unstable. A periodic orbit that is Lyapunov stable is also proven to be always Jacobi unstable. Next, Jacobi-stable regions of the Lorenz system, the Chen system and the system under study are compared for specific parameters. It can be found that although these three chaotic systems are very similar, their regions of Jacobi stable parameters are much different. Finally, by comparing Jacobi stability with Lyapunov stability, the obtained results demonstrate that the Jacobi stable parameter region is basically symmetric with the Lyapunov stable parameter region.

Stochastic Bifurcations, Chaos and Phantom Attractors in the Langford System with Tori

2020 ◽  
Vol 30 (16) ◽  
pp. 2030051
Author(s):  
Irina Bashkirtseva ◽  
Lev Ryashko
Keyword(s):  
Dynamic Model ◽  
Gaussian Noise ◽  
Stochastic Dynamics ◽  
Three Dimensional ◽  
Stochastic Generation ◽  
Noise Amplification ◽  
Quasiperiodic Oscillations ◽  
Stochastic Bifurcations

The variability of stochastic dynamics for a three-dimensional dynamic model in a parametric zone with 2-tori is investigated. It is shown how weak Gaussian noise transforms deterministic quasiperiodic oscillations into noisy bursting. The phenomenon of stochastic generation of a phantom attractor and its shift with noise amplification is revealed. This phenomenon, accompanied by order-chaos transitions, is studied in terms of stochastic [Formula: see text]- and [Formula: see text]-bifurcations.

Constructing a New 3D Chaotic System with Any Number of Equilibria

2019 ◽  
Vol 29 (05) ◽  
pp. 1950060 ◽  
Author(s):  
Qigui Yang ◽  
Xinmei Qiao
Keyword(s):  
Chaotic System ◽  
Chaotic Attractor ◽  
Chaotic Systems ◽  
Stable Equilibrium ◽  
Complex Dynamics ◽  
Type Systems ◽  
Dynamical Behaviors ◽  
Stable Equilibria ◽  
Relationship Of ◽  
Number Of Equilibria

In the chaotic polynomial Lorenz-type systems (including Lorenz, Chen, Lü and Yang systems) and Rössler system, their equilibria are unstable and the number of the hyperbolic equilibria are no more than three. This paper shows how to construct a simple analytic (nonpolynomial) chaotic system that can have any preassigned number of equilibria. A special 3D chaotic system with no equilibrium is first presented and discussed. Using a methodology of adding a constant controller to the third equation of such a chaotic system, it is shown that a chaotic system with any preassigned number of equilibria can be generated. Two complete mathematical characterizations for the number and stability of their equilibria are further rigorously derived and studied. This system is very interesting in the sense that some complex dynamics are found, revealing many amazing properties: (i) a hidden chaotic attractor exists with no equilibria or only one stable equilibrium; (ii) the chaotic attractor coexists with unstable equilibria, including two/five unstable equilibria; (iii) the chaotic attractor coexists with stable equilibria and unstable equilibria, including one stable and two unstable equilibria/94 stable and 93 unstable equilibria; (iv) the chaotic attractor coexists with infinitely many nonhyperbolic isolated equilibria. These results reveal an intrinsic relationship of the global dynamical behaviors with the number and stability of the equilibria of some unusual chaotic systems.

scholarly journals Methods of Stochastic Analysis of Complex Regimes in the 3D Hindmarsh–Rose Neuron Model

2018 ◽  
Vol 17 (01) ◽  
pp. 1850008 ◽  
Author(s):  
Irina Bashkirtseva ◽  
Lev Ryashko ◽  
Evdokia Slepukhina
Keyword(s):  
Stochastic Dynamics ◽  
Random Noise ◽  
Dynamic Regime ◽  
Sensitivity Function ◽  
Interspike Intervals ◽  
Hr Model ◽  
Random States ◽  
Parametric Region ◽  
Good Agreement ◽  
Qualitative Changes

A problem of the stochastic nonlinear analysis of neuronal activity is studied by the example of the Hindmarsh–Rose (HR) model. For the parametric region of tonic spiking oscillations, it is shown that random noise transforms the spiking dynamic regime into the bursting one. This stochastic phenomenon is specified by qualitative changes in distributions of random trajectories and interspike intervals (ISIs). For a quantitative analysis of the noise-induced bursting, we suggest a constructive semi-analytical approach based on the stochastic sensitivity function (SSF) technique and the method of confidence domains that allows us to describe geometrically a distribution of random states around the deterministic attractors. Using this approach, we develop a new algorithm for estimation of critical values for the noise intensity corresponding to the qualitative changes in stochastic dynamics. We show that the obtained estimations are in good agreement with the numerical results. An interplay between noise-induced bursting and transitions from order to chaos is discussed.

scholarly journals Stochastic dynamics for epidemics based on a compartmental scheme: An application to the AH1N1 influenza

2020 ◽  
Vol 66 (6 Nov-Dec) ◽  
pp. 863
Author(s):  
A. Reyes-Romero ◽  
J. E. Fernández ◽  
J. Adrian Reyes
Keyword(s):  
Standard Deviation ◽  
Master Equation ◽  
Probability Density ◽  
Stochastic Dynamics ◽  
Deterministic Model ◽  
Statistical Distributions ◽  
Expected Values ◽  
Influenza Ah1n1 ◽  
Reported Data ◽  
Good Agreement

In this paper a stochastic formulation for describing the dynamics of an epidemic is established. We state our model in the language of a compartmental scheme of three sites (susceptible, infected and recovered) SIR, for which the parameters model are extended to be statistical distributions of time. It is established a master equation for governing the dynamics of the probability density P of finding the system in the state characterized by the values of the aleatory variables S, I, R and time t. Our stochastic formalism allow us to recover the associated deterministic model in terms of the expected values of S, I and R; whereas the second momenta of P provide us statistical standard deviations for these three variables which delimit the region in which most of the particular realizations are to be expected. We have applied the analysis developed here, for studying the specific case of the influenza AH1N1 that took place in Mexico in 2009. The reported data by the main Mexican Health institution are in good agreement with the predictions of our model for the standard deviation of the aleatory variables.

A Free Energy Perturbation Approach to Estimate the Intrinsic Solubilities of Drug-like Small Molecules

2019 ◽  
Author(s):  
Sayan Mondal ◽  
Gary Tresadern ◽  
Jeremy Greenwood ◽  
Byungchan Kim ◽  
Joe Kaus ◽  
...  
Keyword(s):  
Solid State ◽  
Small Molecules ◽  
Three Dimensional ◽  
Aqueous Solubility ◽  
Computational Approach ◽  
Free Energy Perturbation ◽  
Perturbation Approach ◽  
Energy Perturbation ◽  
State Form ◽  
Good Agreement

<p>Optimizing the solubility of small molecules is important in a wide variety of contexts, including in drug discovery where the optimization of aqueous solubility is often crucial to achieve oral bioavailability. In such a context, solubility optimization cannot be successfully pursued by indiscriminate increases in polarity, which would likely reduce permeability and potency. Moreover, increasing polarity may not even improve solubility itself in many cases, if it stabilizes the solid-state form. Here we present a novel physics-based approach to predict the solubility of small molecules, that takes into account three-dimensional solid-state characteristics in addition to polarity. The calculated solubilities are in good agreement with experimental solubilities taken both from the literature as well as from several active pharmaceutical discovery projects. This computational approach enables strategies to optimize solubility by disrupting the three-dimensional solid-state packing of novel chemical matter, illustrated here for an active medicinal chemistry campaign.</p>

A comparative study and combined application of RSM and ANN in adsorptive removal of diuron using biomass ashes

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sunil K. Deokar ◽  
Nachiket A. Gokhale ◽  
Sachin A. Mandavgane
Keyword(s):  
Three Dimensional ◽  
Current Approach ◽  
Coefficient Of Determination ◽  
Ann Model ◽  
Operational Parameters ◽  
Initial Concentration ◽  
Combined Application ◽  
Artificial Neural Network Ann ◽  
Relationship Of ◽  
Biomass Ashes

Abstract Biomass ashes like rice husk ash (RHA), bagasse fly ash (BFA), were used for aqueous phase removal of a pesticide, diuron. Response surface methodology (RSM) and artificial neural network (ANN) were successfully applied to estimate and optimize the conditions for the maximum diuron adsorption using biomass ashes. The effect of operational parameters such as initial concentration (10–30 mg/L); contact time (0.93–16.07 h) and adsorbent dosage (20–308 mg) on adsorption were studied using central composite design (CCD) matrix. Same design was also employed to gain a training set for ANN. The maximum diuron removal of 88.95 and 99.78% was obtained at initial concentration of 15 mg/L, time of 12 h, RHA dosage of 250 mg and at initial concentration of 14 mg/L, time of 13 h, BFA dosage of 60 mg respectively. Estimation of coefficient of determination (R 2) and mean errors obtained for ANN and RSM (R 2 RHA = 0.976, R 2 BFA = 0.943) proved ANN (R 2 RHA = 0.997, R 2 BFA = 0.982) fits better. By employing RSM coupled with ANN model, the qualitative and quantitative activity relationship of experimental data was visualized in three dimensional spaces. The current approach will be instrumental in providing quick preliminary estimations in process and product development.

scholarly journals Simulation of Thermal and Electric Field Distribution in Packaged Sausages Heated in a Stationary Versus a Rotating Microwave Oven

Foods ◽  
2021 ◽  
Vol 10 (7) ◽  
pp. 1622
Author(s):  
Wipawee Tepnatim ◽  
Witchuda Daud ◽  
Pitiya Kamonpatana
Keyword(s):  
Temperature Distribution ◽  
Electric Field ◽  
Three Dimensional ◽  
Development Stage ◽  
Microwave Oven ◽  
Computational Time ◽  
Plastic Package ◽  
Heating Uniformity ◽  
The Cost ◽  
Good Agreement

The microwave oven has become a standard appliance to reheat or cook meals in households and convenience stores. However, the main problem of microwave heating is the non-uniform temperature distribution, which may affect food quality and health safety. A three-dimensional mathematical model was developed to simulate the temperature distribution of four ready-to-eat sausages in a plastic package in a stationary versus a rotating microwave oven, and the model was validated experimentally. COMSOL software was applied to predict sausage temperatures at different orientations for the stationary microwave model, whereas COMSOL and COMSOL in combination with MATLAB software were used for a rotating microwave model. A sausage orientation at 135° with the waveguide was similar to that using the rotating microwave model regarding uniform thermal and electric field distributions. Both rotating models provided good agreement between the predicted and actual values and had greater precision than the stationary model. In addition, the computational time using COMSOL in combination with MATLAB was reduced by 60% compared to COMSOL alone. Consequently, the models could assist food producers and associations in designing packaging materials to prevent leakage of the packaging compound, developing new products and applications to improve product heating uniformity, and reducing the cost and time of the research and development stage.

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