Dynamics of Discrete Time Systems with a Hysteresis Stop Operator

Arnold, Maxim; Begun, Nikita; Gurevich, Pavel; Kwame, Eyram; Lamba, Harbir; Рачинский, Дмитрий

doi:10.1137/16m1073522

Cited by 9 publications

(20 citation statements)

References 59 publications

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“…Equations (1) and (2), completed with formulas (3) and (4), form a closed 3-dimensional PWL model for the evolution of the aggregated variables x t , y t , p t . Another variant of this model has been considered in [36]. Iterations of the system (1)-(4) must start from a set of initial conditions…”

Section: Sticky Expectations Of Inflationmentioning

confidence: 99%

“…First, we add stickiness into the response of the Central Bank (Section 3.2). This can destabilize the equilibrium states (leading to periodic, quasiperiodic or more complex dynamics [36] with associated border collision bifurcations that are typical of piecewise smooth systems [37]) but the system still possesses a bounded globally attracting domain. Then we consider a multi-agent variant of the model (Section 3.3).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The global stability of a class of history-dependent macroeconomic models

Lamba

Krejčı́

Рачинский

2020

Math. Model. Nat. Phenom.

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We consider piecewise-linear, discrete-time, macroeconomic models that have a continuum of feasible equilibrium states. The non-trivial equilibrium set and resulting path-dependence are induced by stickiness in either expectations or the response of the Central Bank. For a low-dimensional variant of the model with one representative agent, and also for a multi-agent model, we show that when exogenous noise is absent from the system the continuum of equilibrium states is the global attractor and each solution trajectory converges exponentially to one of the equilibria. Further, when a uniformly bounded noise is present, or the equilibrium states are destabilized by an imperfect Central Bank policy (or both), we estimate the size of the domain that attracts all the trajectories. The proofs are based on introducing a family of Lyapunov functions and, for the multi-agent model, deriving a formula for the inverse of the Prandtl-Ishlinskii operator acting in the space of discrete-time inputs and outputs.

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Section: Sticky Expectations Of Inflationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The global stability of a class of history-dependent macroeconomic models

Lamba

Krejčı́

Рачинский

2020

Math. Model. Nat. Phenom.

Self Cite

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“…Note that the domain D of existence for the stable fixed point of T (the rightmost segment J 1 is of type I) has been found in [2]:…”

Section: Two-dimensional System With Pwl Saturation Functionmentioning

confidence: 99%

Chaos in Saw Map

Begun

Kravetc

Рачинский

2019

Int. J. Bifurcation Chaos

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We consider dynamics of a scalar piecewise linear "saw map" with infinitely many linear segments. In particular, such maps are generated as a Poincaré map of simple two-dimensional discrete time piecewise linear systems involving a saturation function. Alternatively, these systems can be viewed as a feedback loop with the so-called stop hysteresis operator. We analyze chaotic sets and attractors of the "saw map" depending on its parameters.

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“…Digital systems are modeled as discrete‐time systems. In the last decade, there is a great number of papers published in the famous journals, on the theory and applications of discrete‐time linear time‐varying systems . Therefore, it is very important to investigate the commutativity property for time‐varying discrete‐time systems as well.…”

Section: Introductionmentioning

confidence: 99%

“…In the last decade, there is a great number of papers published in the famous journals, on the theory and applications of discrete-time linear time-varying systems. [16][17][18][19][20][21][22][23][24][25][26][27][28][29] Therefore, it is very important to investigate the commutativity property for time-varying discrete-time systems as well. The paper emphasizes this importance and is aimed to be the first attempt to carry the theory developed for commutativity of analog systems 6 into discrete-time domain.…”

Section: Introductionmentioning

confidence: 99%

Commutativity of first‐order discrete‐time linear time‐varying systems

Köksal

2018

Math Methods in App Sciences

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After introducing the concept of commutativity for continuous‐time linear time‐varying systems, the related literature and the results obtained so far are presented. For a simple introduction of the commutativity of discrete‐time linear time‐varying systems, the problem is formulated for first‐order systems. Finally, explicit necessary and sufficient conditions for the commutativity of first‐order discrete‐time linear time‐varying systems are derived, and their advantageous use in digital system design is illustrated, which are the main objectives of the paper. The results are verified by examples which include an application in amplitude modulation for digital telecommunication.

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Dynamics of Discrete Time Systems with a Hysteresis Stop Operator

Cited by 9 publications

References 59 publications

The global stability of a class of history-dependent macroeconomic models

The global stability of a class of history-dependent macroeconomic models

Chaos in Saw Map

Commutativity of first‐order discrete‐time linear time‐varying systems

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