scholarly journals Dynamics of Systems with a Discontinuous Hysteresis Operator and Interval Translation Maps

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 80
Author(s):  
Sergey Kryzhevich ◽  
Viktor Avrutin ◽  
Nikita Begun ◽  
Dmitrii Rachinskii ◽  
Khosro Tajbakhsh
Keyword(s):  
Risk Management ◽  
Invariant Measure ◽  
Invariant Measures ◽  
Interval Exchange ◽  
Management Model ◽  
Closing Lemma ◽  
Symbolic Model ◽  
Metric Properties ◽  
Ergodic Measures ◽  
Maximal Invariant

We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced the maximal invariant measure and demonstrated that an ITM, endowed with such a measure, is metrically conjugated to an interval exchange map (IEM). This allowed us to extend some properties of IEMs (e.g., an estimate of the number of ergodic measures and the minimality of the symbolic model) to ITMs. Further, we proved a version of the closing lemma and studied how the invariant measures depend on the parameters of the system. These results were illustrated by a simple example or a risk management model where interval translation maps appear naturally.

scholarly journals Invariant measures for interval translations and some other piecewise continuous maps

2020 ◽  
Vol 15 ◽  
pp. 15
Author(s):  
Sergey Kryzhevich
Keyword(s):  
Invariant Measure ◽  
Compact Manifold ◽  
Invariant Measures ◽  
Interval Exchange ◽  
One Dimensional ◽  
Simple Result ◽  
Continuous Maps ◽  
Piecewise Continuous ◽  
Smooth Partition ◽  
Borel Probability

We study some special classes of piecewise continuous maps on a finite smooth partition of a compact manifold and look for invariant measures for such maps. We show that in the simplest one-dimensional case (so-called interval translation maps) a Borel probability non-atomic invariant measure exists for any map. We use this result to demonstrate that any interval translation map endowed with such a measure is metrically equivalent to an interval exchange map. Finally, we study the general case of piecewise continuous maps and prove a simple result on existence of an invariant measure provided all discontinuity points are wandering.

Grid Cyber-Physical System Risk Management Model Based on Cooperative Game Theory

2020 ◽  
Vol 21 (1) ◽  
Author(s):  
Cunbin Li ◽  
Ding Liu ◽  
Yi Wang ◽  
Chunyan Liang
Keyword(s):  
Game Theory ◽  
Risk Management ◽  
Cooperative Game ◽  
Physical System ◽  
Cooperative Game Theory ◽  
Power Grid ◽  
Management Model ◽  
Cyber Physical System ◽  
Model Based ◽  
Generation Power

AbstractAdvanced grid technology represented by smart grid and energy internet is the core feature of the next-generation power grid. The next-generation power grid will be a large-scale cyber-physical system (CPS), which will have a higher level of risk management due to its flexibility in sensing and control. This paper explains the methods and results of a study on grid CPS’s behavior after risk. Firstly, a behavior model based on hybrid automata is built to simulate grid CPS’s risk decisions. Then, a GCPS risk transfer model based on cooperative game theory is built. The model allows decisions to ignore complex network structures. On this basis, a modified applicant-proposing algorithm to achieve risk optimum is proposed. The risk management model proposed in this paper can provide references for power generation and transmission decision after risk as well as risk aversion, an empirical study in north China verifies its validity.

CHAOTIC BEHAVIOR OF HIGHER DIMENSIONAL TRANSFORMATIONS DEFINED ON COUNTABLE PARTITIONS

1993 ◽  
Vol 03 (04) ◽  
pp. 1045-1049
Author(s):  
A. BOYARSKY ◽  
Y. S. LOU
Keyword(s):  
Invariant Measure ◽  
Additional Condition ◽  
Invariant Measures ◽  
Chaotic Behavior ◽  
Finite Collection ◽  
Continuous Invariant Measure ◽  
Absolutely Continuous ◽  
Higher Dimensional ◽  
Absolutely Continuous Invariant Measure ◽  
Absolutely Continuous Invariant

Jablonski maps are higher dimensional maps defined on rectangular partitions with each component a function of only one variable. It is well known that expanding Jablonski maps have absolutely continuous invariant measures. In this note we consider Jablonski maps defined on countable partitions. Such maps occur, for example, in multivariable number theoretic problems. The main result establishes the existence of an absolutely continuous invariant measure for Jablonski maps on a countable partition with the additional condition that the images of all the partition elements form a finite collection. An example is given.

scholarly journals PENGEMBANGAN KERANGKA MANAJEMEN RISIKO PADA PERBANKAN SYARIAH

2019 ◽  
Vol 4 (1) ◽  
pp. 46-67
Author(s):  
Diah Novianti
Keyword(s):  
Decision Making ◽  
Risk Management ◽  
Risk Identification ◽  
The Other ◽  
Management Model ◽  
Islamic Banking ◽  
Business Activity ◽  
Business Risk ◽  
Management Framework ◽  
Risk Management Framework

Islamic banking such as the other business institution will face different kind of risk that inherent on its main business activity. In business, risk defined as a posibillity an can appear every time, before, when, and after the decision making. Islamic banking faced different risk with the conventional banking, because its uniquenes. Thus, the development of risk management framework in Islamic banking is very important to do, especially in frame of  risk identification, measuring, mitigation and monitoring. This paper will discuss about risk management in Islamic Banking, in theoretically and the implementation of risk management. The scope of this study will include the identification of risk in Islamic Banking, stage of risk management in Islamic Banking, risk management model, and also the devolpment of risk management framework in Islamic Banking.

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