Formation of effective investment portfolios on the financial markets: Estimation and management models

The articles deal with consideration of actual issues of formation of effective investment portfolios on the financial markets, in particular, the portfolio of such active institutional investors, as insurance company. The necessity of effectiveness enhancement of investment activity of insurance institutes in the modern conditions was substantiated; the model of insurer’s investment portfolio management, within which the non-linear multi-criteria management task is solved, where criteria include profit maximization and portfolio risk minimization, was developed. The solution of this task, based upon methodological application of theory of non-antagonistic positional differential games. © 2015 Mediterranean Center of Social and Educational Research. All rights reserved

Methods of Stochastic Analysis of Complex Regimes in the 3D Hindmarsh-Rose Neuron Model

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. © 2018 World Scientific Publishing Company.The work was supported by Russian Science Foundation (N 16-11-10098)

Stochastic generation and suppression of early afterdepolarizations in a three-dimensional model of cardiac action potential

The influence of random disturbances on a three-dimensional simplification of Luo–Rudy model of the cardiac action potential is studied. We show that in the parameter region, where the deterministic model is in the equilibrium regime, noise can trigger large-amplitude oscillations that correspond with pathological early afterdepolarizations (EADs). For this stochastic excitement, the phenomenon of coherence resonance was discovered. On the contrary, in another parameter zone of the model, noise can suppress EADs. We analyze these stochastic phenomena using the stochastic sensitivity functions technique, Mahalanobis distance, the methods of principal directions, and confidence domains. © 2021 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons, Ltd.Russian Science Foundation, RSF: 21-11-00062This work was supported by the Russian Science Foundation (No. 21-11-00062)

Analysis of additive and parametric noise effects on Morris - Lecar neuron model

This paper is devoted to the analysis of the effect of additive and parametric noise on the processes occurring in the nerve cell. This study is carried out on the example of the well-known Morris - Lecar model described by the two-dimensional system of ordinary differential equations. One of the main properties of the neuron is the excitability, i.e., the ability to respond to external stimuli with an abrupt change of the electric potential on the cell membrane. This article considers a set of parameters, wherein the model exhibits the class 2 excitability. The dynamics of the system is studied under variation of the external current parameter. We consider two parametric zones: the monostability zone, where a stable equilibrium is the only attractor of the deterministic system, and the bistability zone, characterized by the coexistence of a stable equilibrium and a limit cycle. We show that in both cases random disturbances result in the phenomenon of the stochastic generation of mixed-mode oscillations (i. e., alternating oscillations of small and large amplitudes). In the monostability zone this phenomenon is associated with a high excitability of the system, while in the bistability zone, it occurs due to noise-induced transitions between attractors. This phenomenon is confirmed by changes of probability density functions for distribution of random trajectories, power spectral densities and interspike intervals statistics. The action of additive and parametric noise is compared. We show that under the parametric noise, the stochastic generation of mixed-mode oscillations is observed at lower intensities than under the additive noise. For the quantitative analysis of these stochastic phenomena we propose and apply an approach based on the stochastic sensitivity function technique and the method of confidence domains. In the case of a stable equilibrium, this confidence domain is an ellipse. For the stable limit cycle, this domain is a confidence band. The study of the mutual location of confidence bands and the boundary separating the basins of attraction for different noise intensities allows us to predict the emergence of noise-induced transitions. The effectiveness of this analytical approach is confirmed by the good agreement of theoretical estimations with results of direct numerical simulations. © 2017 Lev B. Ryashko, Evdokia S. Slepukhina.The work was supported by the Government of the Russian Federation (Act 211, contract No. Russian Foundation for Basic Research (project No. 16-31-00317 mol_a)

Constructive role of noise and diffusion in an excitable slow-fast population system

We study the effects of noise and diffusion in an excitable slow-fast population system of the Leslie-Gower type. The phenomenon of noise-induced excitement is investigated in the zone of stable equilibria near the Andronov-Hopf bifurcation with the Canard explosion. The stochastic generation of mixed-mode oscillations is studied by numerical simulation and stochastic sensitivity analysis. Effects of the diffusion are considered for the spatially distributed variant of this slow-fast population model. The phenomenon of the diffusion-induced generation of spatial patterns-attractors in the Turing instability zone is demonstrated. The multistability and variety of transient processes of the pattern formation are discussed. © 2020 The Author(s) Published by the Royal Society. All rights reserved.Russian Science Foundation, RSF: 16-11-10098Data accessibility. This article does not contain any additional data. Authors’ contributions. All authors contributed equally to this study. Competing interests. We declare we have no competing interests. Funding. The work was supported by Russian Science Foundation (grant no. 16-11-10098)

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

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. © 2016 World Scientific Publishing Company

Stochastic Generation of Large-Amplitude Oscillations in a Three-Dimensional Model of Cold-Flame Combustion of a Hydrocarbon Mixture

We study a stochastic 3D model of cold-flame combustion of a hydrocarbon mixture. We show that noise can induce large-amplitude oscillations from the equilibrium regime. We analyze this phenomenon by means of the stochastic sensitivity function technique and the method of confidence domains.Исследование выполнено за счет гранта РФФИ (проект № 20-01-00165)

STOCHASTIC OSCILLATIONS NEAR THE “BLUE SKY CATASTROPHE” BIFURCATION IN NEURON MODEL

We study the stochastic Hindmarsh-Rose neuron model near the “blue sky catastrophe” bifurcation. This specific bifurcation describes a particular type of transition between tonic spiking and bursting oscillations in the considered model. We show that noise can induce the changes of frequency and amplitude characteristics of bursting oscillations in this model. Moreover, in the parameter zone of tonic spiking regime, the increase of the noise intensity can lead to the stochastic generation of bursting oscillations. We perform the analysis of these phenomena on the base of the stochastic sensitivity functions technique and the confidence domains method.Исследование выполнено за счет гранта Российского научного фонда (проект № 16-11-10098)

NOISE-INDUCED QUASI-PERIODIC OSCILLATIONS IN HINDMARSH-ROSE NEURON MODEL

We study the phenomenon of noise-induced quasi-periodic oscillations in the stochastic Hindmarsh-Rose neuron model. We show that with the increase of the noise intensity the periodic regime in this model transforms into the quasi-periodic one with the formation of the stochastic torus. We perform the analysis of this phenomenon on the base of the stochastic sensitivity functions technique and the confidence domains method

STOCHASTIC GENERATION OF EARLY AFTERDEPOLARIZATIONS IN A THREE-DIMENSIONAL MODEL OF CARDIAC ACTION POTENTIAL IN A QUIESCENT MODE

We study a stochastic three-dimensional model of cardiac action potential. We show that noise can induce pathological early afterdepolarizations in a quiescent mode. We analyze this phenomenon by means of statistics of interspike intervals and the stochastic sensitivity functions method