New Characteristic Relations in Type-II and III Intermittency

Abstract

We obtained new characteristic relations in Type-II and III intermittencies according to the reinjection probability distribution. When the reinjection probability distribution is fixed at the lower bound of reinjection, the critical exponents are -1, as is well known. However when the reinjection probability distribution is uniform, the critical exponent is -1/2, and when it is of form [Formula: see text], -3/4. On the other hand, if the square root of Δ, which represents the lower bound of reinjection, is much smaller than the control parameter ∊, i.e. ∊ ≫ Δ1/2, critical exponent is always -1, independent of the reinjection probability distribution. Those critical exponents are confirmed by numerical simulation study.

Characteristic Relations of Type-III Intermittency in an Electronic Circuit

“…In the case of type-II and III intermittencies, the characteristic relations also have various critical exponents for a given local Poincaré map such as e 2n ͑1͞2 # n # 1͒ dependent on the RPD. When RPDs are uniform, of the form x 21͞2 around the tangent point, and fixed very close to the tangent point, the characteristic relations are e 21͞2 , e 23͞4 , and e 21 , respectively [6]. In this report we discuss the characteristic relations of type-III intermittency analytically, and obtain e 21͞2 characteristic relation experimentally in an electronic circuit that consists of inductor, resistor, and diode with uniform RPD.…”

Calculation of Invariant Manifolds of Piecewise-Smooth Maps

“…Таким образом, для любой точки (х, y) ∈ Dℳ обратная итерация Fℳ выполняется в два шага: сначала по (x', y') вычисляется z (0 < z < 1.0), численно решив уравнение (10). Полученное z подставляется в (6).…”

“…Для изучения нелинейных явлений в мультистабильных системах требуется найти специальные инвариантные множества, такие как репеллеры, седловые периодические орбиты вместе с их устойчивыми и неустойчивыми многообразиями, играющие ключевую роль в глобальной динамике [8][9][10]. Устойчивые и неустойчивые инвариантные многообразия нельзя рассчитать ни аналитически, ни с помощью техники линеаризации.…”

Effect of the lower boundary of reinjection and noise in Type-II intermittency

“…Type-II intermittency was found in a driven double scroll circuit as a consequence of a global bifurcation scenario for T 2 torus breakdown [25,26]. Also, characteristic relations for type-II intermittency were studied in [27]. The noise effect on the intermittency phenomenon was studied using renormalization group analysis or by using the Fokker-Plank equation [28][29][30].…”