1,721,937 research outputs found
Noise-induced shifts in the ecological model with delay
Get PDFA Hassell-type mathematical model of population dynamics with delay and stochastic disturbances is considered. In this bistable model, one of the attractors corresponds to the extinction, and the other one describes non-trivial stable modes of dynamics. These modes can be both regular and chaotic. Structural stability zones are separated by local and global bifurcations. We study how noise shifts these bifurcation points and contracts the persistence zone. Abilities of the theoretical analysis of these phenomena with the help of the stochastic sensitivity function technique is discussed. © 2019 Author(s).Russian Science Foundation, RSF: N 16-11-10098The work was supported by Russian Science Foundation (N 16-11-10098)
Analysis of the stochastically forced invariant manifolds of dynamic systems
Get PDFWe consider the randomly forced invariant manifolds of nonlinear dynamic systems. To study the dispersion of random states near the general deterministic attractors, we discuss two approaches. The first approach is based on the approximation of the quasipotential, and the second one uses the linear extension systems. A new semi-analytical method based on the stochastic sensitivity functions is suggested. The corresponding mathematical theory is shortly presented. Constructive applications of this theory to the analysis of equilibria and oscillatory regimes are given. © 2017 Author(s).The work was supported by Russian Science Foundation (No 16-11-10098)
Variability and effect of noise on the corporate dynamics of coupled oscillators
Get PDFA nonlinear dynamical model of two coupled neurons based on the Rulkov map is considered. Variability analysis of corporate dynamics depending on the type of activity of separated neurons and strength of coupling is performed. Transitions between stationary, periodic, quasiperiodic, and chaotic regimes of this neuron system are studied. Additional effects of random disturbances on this system are discussed. Noise-induced transitions between periodic and chaotic stochastic oscillations are demonstrated. © 2019 Author(s).Russian Science Foundation, RSF: N 16-11-10098The work was supported by Russian Science Foundation (N 16-11-10098)
Analysis of stochastic phenomena in Ricker-type population model with delay
Get PDFA phenomenon of the noiseinduced extinction is studied on the base of the conceptual Rickertype model with the delay and Allee effect. This nonlinear discrete population model exhibits the persistence with the different form of attractors, both regular and chaotic. For this model, the persistence zones are defined by points of the crisis bifurcations. The phenomenon of the noiseinduced extinction is investigated with the help of direct numerical simulations and by the semianalytical new method based on the stochastic sensitivity functions. In the stochastic analysis, a geometrical approach taking into account a mutual arrangement of the confidence domains and basins of attraction is used. © 2017 Author(s).The work was supported by Russian Science Foundation (grant No 16-11-10098)
Stochastic phenomena in pattern formation for distributed nonlinear systems
Get PDFWe study a stochastic spatially extended population model with diffusion, where we find the coexistence of multiple non-homogeneous spatial structures in the areas of Turing instability. Transient processes of pattern generation are studied in detail. We also investigate the influence of random perturbations on the pattern formation. Scenarios of noise-induced pattern generation and stochastic transformations are studied using numerical simulations and modality analysis. © 2020 The Author(s) Published by the Royal Society. All rights reserved.Russian Science Foundation, RSF: 16-11-10098Data accessibility. This article has no additional data. Authors’ contributions. All authors contributed equally. Competing interests. We declare we have no competing interests. Funding. The work was supported by the Russian Science Foundation (grant no. 16-11-10098)
Stochastic phenomena in the dynamical tumor-immune system
Get PDFA nonlinear dynamical model describing the interaction of tumor and immune cells is considered. Regimes of "dormant tumor" and "tumor explosion" are studied by methods of the bifurcation theory and stochastic simulation. Noise-induced transitions from "dormant tumor" to "tumor explosion" and back are investigated parametrically in dependence of the noise intensity and parameter of the inactivation of immune cells by tumor ones. Three scenarios of the noise-induced transitions are discussed: (i) from "dormant tumor" to "tumor explosion", (ii) from "tumor explosion" to "dormant tumor", (iii) oscillations between these two regimes. © 2019 Author(s).Russian Science Foundation, RSF: N 16-11-10098The work was supported by Russian Science Foundation (N 16-11-10098)
Stochastic sensitivity analysis of noise-induced oscillations in Adler model
Get PDFWe consider Adler model with the saddle-node bifurcation on the invariant circle. Near this bifurcation, even weak random disturbances can generate noise-induced spike oscillations. Corresponding random phase trajectories form stochastic bundle. A dispersion of random trajectories in this bundle is non-uniform. To approximate this dispersion, we propose a new constructive approach based on the stochastic sensitivity analysis and method of "freezing" of the phase variable. A mathematical description of this approach is given. An extension of this theory for complex systems with so-called sequential dynamics is discussed. © 2019 Author(s).Russian Science Foundation, RSF: N 16-11-10098The work was supported by Russian Science Foundation (N 16-11-10098)
STOCHASTIC ANALYSIS OF THE RICKER POPULATION MODEL WITH IMMIGRATION AND ALLEE EFFECT
Get PDFWe study an impact of the immigration on population dynamics of the Ricker model with Allee effect. Both deterministic and stochastic cases of the model are considered.Исследование выполнено при поддержке РНФ (грант 16-11-10098)
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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