Akhmet, Marat
Tleubergenova, M.
Zhamanshin, A.
The existence of unpredictable motions in systems of quasilinear differential equations with hyperbolic linear part is rigorously proved. We make use of the topology of uniform convergence on compact sets and the contraction mapping principle to prove the existence of unpredictable motions. Appropriate examples with simulations that support the theoretical results are provided.


Oscillation of Higher-Order Neutral-Type Periodic Differential Equations with Distributed Arguments
Dahiya, R. S.; Zafer, A. (Springer Science and Business Media LLC, 2007)
We derive oscillation criteria for general-type neutral differential equations [x(t) +αx(t− τ) +βx(t +τ)](n) = δ b ax(t − s)dsq1(t,s) + δ d c x(t + s)dsq2(t,s) = 0, t ≥ t0, where t0 ≥ 0, δ = ±1, τ > 0, b>a ≥ 0, d>c ≥ 0, α and β are real numbers, the functions q1(t,s) : [t0,∞) × [a,b] → R and q2(t,s):[t0,∞) × [c,d] → R are nondecreasing in s for each fixed t, and τ is periodic and continuous with respect to t for each fixed s. In certain special cases, the results obtained generalize and improve s...
Oscillation of nonlinear impulsive partial difference equations with continuous variables
Agarwal, R. P.; KARAKOÇ, FATMA; Zafer, Ağacık (Informa UK Limited, 2012-01-01)
By employing a difference inequality without impulses, we establish several sufficient conditions for the oscillation of solutions of a class of nonlinear impulsive partial difference equations with continuous variables.
Time scale extensions of a theorem of Wintner on systems with asymptotic equilibrium
Mert, R.; Zafer, Ağacık (Informa UK Limited, 2011-01-01)
Abstract We consider quasilinear dynamic systems of the form[image omitted]where is a time scale, and provide extensions of a theorem of Wintner on systems with asymptotic equilibrium to arbitrary time scales. More specifically, we give sufficient conditions for the asymptotic equilibrium of the above system in the sense that for any given constant vector c, there is a solution satisfying[image omitted] Our results are new for difference equations, q-difference equations and many other time scale systems ev...
Oscillation for a nonlinear dynamic system on time scales
Erbe, Lynn; Mert, Raziye (Informa UK Limited, 2011-01-01)
We study the oscillation properties of a system of two first-order nonlinear equations on time scales. This form includes the classical Emden-Fowler differential and difference equations and many of its extensions. We generalize some well-known results of Atkinson, Belohorec, Waltman, Hooker, Patula and others and also describe the relation to solutions of a delay-dynamic system.
On Lyapunov inequality in stability theory for Hill's equation on time scales
Atici, FM; Guseinov, GS; Kaymakcalan, B (Springer Science and Business Media LLC, 2000-01-01)
In this paper we obtain sufficient conditions for instability and stability to hold for second order linear Delta -differential equations on time scales with periodic coefficients.
Citation Formats
M. Akhmet, M. Tleubergenova, and A. Zhamanshin, “POINCARE CHAOS FOR A HYPERBOLIC QUASILINEAR SYSTEM,” MISKOLC MATHEMATICAL NOTES, pp. 33–44, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/39119.