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We consider the wrinkling of highly stretched, thin rectangular sheets – a problem that has attracted the attention of several investigators in recent years, nearly all of which employ the classical Föppl-von Kármán (F-K) theory of plates. (See Figure 1 below for a schematic diagram.) We first propose a rational model that correctly accounts for large(More)
β 0 x(⟦t⟧) − β 1 x(⟦t − 1⟧)) + γ 1 x(⟦t⟧) + γ 2 x(⟦t − 1⟧)}, where the parameters α, β 0 , β 1 , and r denote positive numbers, γ 1 and γ 2 are negative numbers and ⟦t⟧ is the integer part of t ∈ [0,∞). Equation (A) explains a brain tumor growth, where γ 1 is embedded to show the drug effect on the tumor and γ 2 is a rate that causes a negative effect by(More)
Smale horseshoes, curvilinear rectangles and their U-shaped images patterned on Smale’s famous example, provide a rigorous way to study chaos in dynamical systems. The paper is devoted to constructing them in two-dimensional diffeomorphisms with the existence of transversal homoclinic saddles. We first propose an algorithm to automatically construct(More)
This paper uncovers several new stable periodic gaits in the simplest passive walking bipedal model proposed in the literature. It is demonstrated that the model has period-3 to period-7 gaits beside the period-1 gaits found by Garcia et al. By simulations, this paper shows that each of these new gaits leads to chaos via period-doubling bifurcation and(More)