László Hatvani

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The present paper is devoted to studying Hubbard’s pendulum equation ẍ + 10−1ẋ + sin(x) = cos(t) . Using rigorous/interval methods of computation, the main assertion of Hubbard on chaos properties of the induced dynamics is raised from the level of experimentally observed facts to the level of a theorem completely proved. A special family of solutions is(More)
where a : R+ → R+ is a positive nondecreasing function. This equation describes the motion of a material point of unit mass under the action of restoring force with changing elasticity coefficient. It is known [11] that every solution x of (L) is oscillatory, the maxima of |x| do not increase and the maxima of |x′| do not decrease as t goes to infinity. The(More)
In this paper we give a sufficient condition to imply global asymptotic stability of a delayed cellular neural network of the form ẋi(t) = −dixi(t) + n ∑ j=1 aijf(xj(t)) + n ∑ j=1 bijf(xj(t− τij)) + ui, t ≥ 0, i = 1, . . . , n, where f(t) = 1 2 (|t+1|− |t−1|). In order to prove this stability result we need a sufficient condition which guarantees that the(More)
We report on the first steps made towards the computational proof of the chaotic behavior of the forced damped pendulum. Although, chaos for this pendulum was being conjectured for long, and it has been plausible on the basis of numerical simulations, there is no rigorous proof for it. In the present paper we provide computational details on a fitting model(More)
The present paper is devoted to studying Hubbard’s pendulum equation ẍ+ 10ẋ+ sin(x) = cos(t) . By rigorous/interval methods of computation, the main assertion of Hubbard on chaos properties of the induced dynamics is lifted from the level of experimentally observed facts to the level of a theorem completely proved. A distinguished family of solutions is(More)
The authors consider the three point boundary value problem consisting of the nonlinear differential equation u(t) = g(t)f(u), 0 < t < 1, (E) and the boundary conditions u(0) = u(1) = u(1) = u(0) − u(p) = 0. (B) Sufficient conditions for the existence of multiple positive solutions to the problem (E)–(B) are given. This paper is in final form and no version(More)
In this paper, we obtain new observability inequalities for the vibrating string. This work was motivated by a recent paper of Szijártó and Hegedűs in which the authors ask the question of determining the initial data by only knowing the position of the string at two distinct time instants. The choice of the observation instants is crucial and the(More)