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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)
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)
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)
Chua’s circuit has becomes very popular since the mid-1980’s [Mees & Chapman, 1987; Zhong & Ayrom, 1985; Kennedy, 1993a, 1993b; Shil’nikov, 1993; Brown, 1993; Belykh & Chua, 1993], because it is a rather simple electronic system that exhibits chaos. Due to its physical nature, Chua’s circuit is an ideal paradigm for research on chaos by laboratory(More)