Browsing by Author "Nategh, Mehdi"

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Almost local stability in discrete delayed chaotic systems
(Springer, 2017) Nategh, Mehdi; Baleanu, Dumitru; Baleanu, Dumitru; Taghizadeh, Elham; Gilani, Zahra Goli
This work studies dynamic of delayed discrete chaotic systems with bounded and unbounded delays. The time lags appear in additive which is coupled with a smooth function and nonadditive forms. It has been shown that, in both additive and nonadditive cases, the primal (non-delayed) system is neutral to the bounded delay to possess an attractive fixed point. Nevertheless, if a nonadditive and unbounded delay is supposed to affect a chaotic and measure preserving system locally, then the delay function might be sensitive to initial states. A local stabilization to the dynamics of Logistic and Gaussian maps are made and creation of attractive fixed points is illustrated.
Non-integer variable order dynamic equations on time scales involving caputo-fabrizio type differential operator
(2018) Baleanu, Dumitru; Nategh, Mehdi; 56389
This work deals with the conecept of a Caputo-Fabrizio type non-integer variable order differential opertor on time scales that involves a non-singular kernel. A measure theoretic discussion on the limit cases for the order of differentiation is presented. Then, corresponding to the fractional derivative, we discuss on an integral for constant and variable orders. Beside the obtaining solutions to some dynamic problems on time scales involving the proposed derivative, a fractional folrmulation for the viscoelastic oscillation problem is studied and its conversion into a third order dynamic equation is presented. © 2018 by Eudoxus Press, LLC. All rights reserved.
On a discrete chaos induction via an aperiodic kicks pattern
(Asme, 2017) Nategh, Mehdi; Baleanu, Dumitru; Baleanu, Dumitru; Valinejad, Mohammad Reza; 56389
In this work, a class of kicked systems perturbed with an irregular kicks pattern is studied and formation of a chaos in the senses of Devaney and Li-Yorke in the corresponding discretized system is investigated. Beside a discussion on chaotic stability, an example is presented. Then, the existence of a period three orbit of a 2D map which governs a class of dynamic problems on time scales is studied. As an application, a chaotic encryption scheme for a time-dependent plain text with the help of chaos induction in the sense of Li-Yorke is presented.
Population dynamic caused by war involvement via fractional derivative on time scales
(Inderscience Enterprises LTD, 2019) Baleanu, Dumitru; Baleanu, Dumitru; Neamaty, Abdolali; Agheli, Bahram; 56389
This work suggests a model for a population dynamic caused by an enemy attack to a domain of residential areas. With the help of a local non-integer order rate of change and a new structure induced on the real line, we derive a spatial discrete diffusion equation of fractional order. Then making use of the d'Alembert's change of variable we obtain a time scale which is made of union of disjoint compact intervals. These considerations lead us to a non-homogeneous second order nonlinear differential equation. The existence of a positive solution is discussed and through a numerical example the theory is illustrated.