On classification of classical and half-orientable horseshoes in terms of boundary points

Гонченко, С. В.; Gonchenko, A. S.; Malkin, Mikhail

doi:10.20537/nd1003006

Cited by 5 publications

(2 citation statements)

References 4 publications

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“…The segment includes a scattered continuum set of subintervals from two attraction regions Ω 1 and Ω 2 of two attractors Λ 1 and Λ 2 , but the boundaries of all subintervals do not belong to these attraction regions and form an invariant set-a strange repeller. There are a number of chaotic regimes in the dynamics of iterations that are not associated with closed attracting sets, these being the phenomena of "horseshoe dynamics" or the effect of "chaotic scattering" [29].…”

Section: Features Of the Phase Portrait Of A Hybrid Dynamical Systemmentioning

confidence: 99%

Modeling of a Crisis in the Biophysical Process by the Method of Predicative Hybrid Structures

Perevaryukha

2022

Tech. Phys.

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Crisis processes of biosystems often develop according to scenarios of rapid collapse, which cannot be predicted by statistical methods. This paper develops a method for constructing hybrid computational models using event-hierarchy representation for biophysical processes. System events calculated by the algorithm change the order of calculation of equations according to a given set of rules. The rules of physically conditioned redefinition of the right-hand sides of differential equations are used. The predicates employ the calculations of a group of accompanying characteristics, which are an integral part of the controlled biophysical dynamics. The model is investigated by presenting a computational scenario with a set of parameters, initial values, and an algorithm for making decisions about changing the impact for discrete time. Using computational experiments, a real outcome scenario for a situation that leads to the collapse of a biophysical system at a controlled level of exposure is described. The scenario sets the logic for making control decisions to change the level of external pressure on the natural environment. It is shown as a result of modeling that the transition of the process to an oscillatory mode leads to the choice of a risky control mode. It has been established that the dynamics of many real water populations has a point of threshold reduction in the efficiency of replenishment of stocks. The model scenario uses transformations of the phase portrait of iterations, which, in the presence of disconnected boundaries of the areas of attraction of alternative attractors and a strange chaotic repeller, lead to the uncertainty effects arising due to chaotic modes in a deterministic model. The properties of the described model scenario with a chaotic regime of dynamics are confirmed by the example of the catch of oceanic species of crustaceans.

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Section: Features Of the Phase Portrait Of A Hybrid Dynamical Systemmentioning

confidence: 99%

Modeling of a Crisis in the Biophysical Process by the Method of Predicative Hybrid Structures

Perevaryukha

2022

Tech. Phys.

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“…The degeneracy of the Hénon map is canceled in GHM at nonzero ν 1 (see [53]), so the analysis of this map provides an accurate information on the birth of closed invarant curves near homoclinic tangencies [46,48,[50][51][52]55], homoclinic loops [56], and heteroclinic cycles [54]. Note also that map (1.5) at ν 1,2 not small demonstrates interesting hyperbolic dynamics (the so-called half-orientable horseshoes) [57][58][59].…”

Section: Introductionmentioning

confidence: 99%

Examples of Lorenz-like Attractors in Hénon-like Maps

Гонченко

Gonchenko

Ovsyannikov

et al. 2013

Math. Model. Nat. Phenom.

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We display a gallery of Lorenz-like attractors that emerge in a class of threedimensional maps. We review the theory of Lorenz-like attractors for diffeomorphisms (as opposed to flows), define various types of such attractors, and find sufficient conditions for three-dimensional Henon-like maps to possess pseudohyperbolic Lorenz-like attractors. The numerically obtained scenarios of the creation and destruction of these attractors are also presented.

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On the Formation of a Hierarchical Event Representation of Hybrid Time for Simulation of Extreme Threshold Development of Physical Processes

Perevaryukha

2022

Tech. Phys. Lett.

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On classification of classical and half-orientable horseshoes in terms of boundary points

Cited by 5 publications

References 4 publications

Modeling of a Crisis in the Biophysical Process by the Method of Predicative Hybrid Structures

Modeling of a Crisis in the Biophysical Process by the Method of Predicative Hybrid Structures

Examples of Lorenz-like Attractors in Hénon-like Maps

On the Formation of a Hierarchical Event Representation of Hybrid Time for Simulation of Extreme Threshold Development of Physical Processes

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