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The periodic character in a higher order difference equation with delays

Gümüş M.

Article | 2019 | Mathematical Methods in the Applied Sciences

The aim of this paper is to investigate the global dynamics of the delay nonlinear difference equation (Formula presented.) where k, l, and m are positive integers, the parameters A, B, C, p, and q are nonnegative real numbers, and the initial values (Formula presented.) are nonnegative real numbers such that the denominator is always positive. Several numerical simulations are provided to support obtained results. Also, our results extend and generalize the known ones. © 2019 John Wiley & Sons, Ltd.

THE DYNAMICS OF POSITIVE SOLUTIONS OF A HIGHER ORDER FRACTIONAL DIFFERENCE EQUATION WITH ARBITRARY POWERS

Gumus, Mehmet | Soykan, Yuksel

Article | 2017 | JOURNAL OF APPLIED MATHEMATICS & INFORMATICS35 ( 03.Apr ) , pp.267 - 276

The purpose of this paper is to investigate the local asymptotic stability of equilibria, the periodic nature of solutions, the existence of unbounded solutions and the global behavior of solutions of the fractional difference equation x(n+1) = alpha xn-(k+1)/beta+gamma x(n)(p) (k)x(n)(g)-(k+2), n =0,1... where the parameters alpha, beta, gamma; p, q are non-negative numbers and the initial values x - (k + 2), x -(k + 1),..., x-1; x(0) is an element of R+.

Synchronization induced termination in neuronal networks

Çalım, Ali | Ağaoğlu, Şükriye Nihal | Uzuntarla, Muhammet

Proceedings | 2017 | 2017 25th Signal Processing and Communications Applications Conference, SIU 2017 , pp.267 - 276

Vital functions which take place in the brain are accomplished through synchronized neural activities between interconnected neuronal populations. In healthy and unhealthy nerve system, rhythms in different frequencies can be recognized as they are responsible for neural synchronization. Despite this, in the case of global synchronization where oscillation power is the maximum, as observed in epileptic seizures, neural activity can terminate. In this study, effects of neural network characteristics synchronization emerges from on activity termination are computationally investigated. Stochastic Hodgkin-Huxley (H-H) equations are use . . .d in the simulations. The results show that synchronization increases when neurons have high synaptic conductance and due to this, strong synaptic current neurons exposed to terminates the firings. © 2017 IEEE Daha fazlası Daha az

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