Difference equations with impulses

Danca, Marius‐F.; Fečkan, Michal; Pospíšil, Michal

doi:10.7494/opmath.2019.39.1.5

Cited by 6 publications

(4 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In general, it is difficult to find fixed points. As presented in this paper (see also [29]), for concrete parameters, the fixed points can be found numerically.…”

Section: Analytical Study Of the Impulsed Supply And Demand Systemmentioning

confidence: 85%

“…On the other side, for general systems, small perturbations may lead to unbounded oscillations for particular values of parameters. Summarizing, one concludes that for every ∆ and γ, the impulsed system (2) has bounded orbits and there exist periodic orbits (see [29] for more details on difference equations with impulses).…”

Section: Analytical Study Of the Impulsed Supply And Demand Systemmentioning

confidence: 86%

See 1 more Smart Citation

Hidden chaotic attractors and chaos suppression in an impulsive discrete economical supply and demand dynamical system

Danca

Fečkan

2019

Communications in Nonlinear Science and Numerical Simulation

Self Cite

View full text Add to dashboard Cite

Impulsive control is used to suppress the chaotic behavior in an one-dimensional discrete supply and demand dynamical system. By perturbing periodically the state variable with constant impulses, the chaos can be suppressed. It is proved analytically that the obtained orbits are bounded and periodic. Moreover, it is shown for the first time that the difference equations with impulses, used to control the chaos, can generate hidden chaotic attractors. To the best of the authors knowledge, this interesting feature has not yet been discussed. The impulsive algorithm can be used to stabilize chaos in other classes of discrete dynamical systems.

show abstract

“…In general, it is difficult to find fixed points. As presented in this paper (see also [29]), for concrete parameters, the fixed points can be found numerically.…”

Section: Analytical Study Of the Impulsed Supply And Demand Systemmentioning

confidence: 85%

Section: Analytical Study Of the Impulsed Supply And Demand Systemmentioning

confidence: 86%

Hidden chaotic attractors and chaos suppression in an impulsive discrete economical supply and demand dynamical system

Danca

Fečkan

2019

Communications in Nonlinear Science and Numerical Simulation

Self Cite

View full text Add to dashboard Cite

show abstract

“…At the same time impulses are a very useful mathematical apparatus to model some instantaneous perturbations in the process (see, for example [5], [11]). Difference equations, being a discrete version of differential equations, could have also impulses (see, for example, [8]). In the case when the acting time of the impulses is not possible to be neglected, these impulses are called non-instantaneous impulses (for continuous case, see, [2], [3]).…”

Section: Introductionmentioning

confidence: 99%

Exponential Stability of Discrete Neural Networks With Non-Instantaneous Impulses, Delays and Variable Connection Weights With Computer Simulation

Hristova¹,

Stefanova²

2020

Int. J. of Appl. Math.

View full text Add to dashboard Cite

The exponential stability concept for nonlinear non-instantaneous impulsive difference equations with a single delay is studied and some criteria are derived. These results are also applied for a neural networks with switching topology at certain moments and long time lasting impulses. It is considered the general case of time varying connection weights. The equilibrium is defined and exponential stability is studied. The obtained results are illustrated on examples.

show abstract

“…Impulsive equations modeled with continuous or discontinuous differential equations of integer order or fractional order [17,18,19,20], or by discrete equations [21] have been developed in impulsive problems in physics, orbital transfer of satellite, population dynamics, dosage supply in pharmacokinetics, biotechnology, pharmacokinetics, ecosystems management, industrial robotics, synchronization in chaotic secure communication systems, and so forth (see [7] for a deep background on impulsive differential equations and inclusions and references, or [6]).…”

Section: Introductionmentioning

confidence: 99%

Chaos control in the fractional order logistic map via impulses

2019

Self Cite

View full text Add to dashboard Cite

In this paper the chaos control in the discrete logistic map of fractional order is obtained with an impulsive control algorithm. The underlying discrete initial value problem of fractional order is considered in terms of Caputo delta fractional difference. Every ∆ steps, the state variable is instantly modified with the same impulse value, chosen from a bifurcation diagram versus impulse. It is shown that the solution of the impulsive control is bounded. The numerical results are verified via time series, histograms, and the 0-1 test. Several examples are considered.keyword Caputo delta fractional difference; Impulsive chaos control; Discrete logistic map of fractional order; Lyapunov exponent of discrete maps of fractional order; 0-1 test Marius-F. Danca

show abstract

Difference equations with impulses

Cited by 6 publications

References 9 publications

Hidden chaotic attractors and chaos suppression in an impulsive discrete economical supply and demand dynamical system

Hidden chaotic attractors and chaos suppression in an impulsive discrete economical supply and demand dynamical system

Exponential Stability of Discrete Neural Networks With Non-Instantaneous Impulses, Delays and Variable Connection Weights With Computer Simulation

Chaos control in the fractional order logistic map via impulses

Contact Info

Product

Resources

About