Kaotička i kvaziperiodična rješenja robotičke jednadžbe s jednim stupnjem slobode

For the first time a possibility of chaotic regime for a robotic equation is investigated, using equation for a model of robot with one degree of freedom with viscous and dry friction and hard-spring rigidity. The transient motion was not excluded in this investigation. A chaotic regime is discovered in a particular scan, with enhanced rigidity, for the critical length parameter Lc which exceeds the upper limit of L in the standard parameter range by a factor of ≈ 50. In the chaotic regime a pronounced period three window is found.Po prvi put istražvana je mogućnost kaotičkog režima za robotičku jednadžbu, koristeći jednadžbu za model robota s jednim stupnjem slobode uz viskozno i suho trenje i krutosti tvrde opruge. U istraživanju nije isključeno tranzijentno gibanje. Kaotički režim je otkriven u specijalnom području parametara, s povećanom krutošću, za kritičku vrijednost parametra duljine Le koji za 50% premašuje gornju granicu u standardnom rasponu parametara. U kaotičkom režimu otkriven je naglašeni prozor regularnosti s periodom tri

Kaotička i kvaziperiodična rješenja robotičke jednadžbe s jednim stupnjem slobode

For the first time a possibility of chaotic regime for a robotic equation is investigated, using equation for a model of robot with one degree of freedom with viscous and dry friction and hard-spring rigidity. The transient motion was not excluded in this investigation. A chaotic regime is discovered in a particular scan, with enhanced rigidity, for the critical length parameter Lc which exceeds the upper limit of L in the standard parameter range by a factor of ≈ 50. In the chaotic regime a pronounced period three window is found.Po prvi put istražvana je mogućnost kaotičkog režima za robotičku jednadžbu, koristeći jednadžbu za model robota s jednim stupnjem slobode uz viskozno i suho trenje i krutosti tvrde opruge. U istraživanju nije isključeno tranzijentno gibanje. Kaotički režim je otkriven u specijalnom području parametara, s povećanom krutošću, za kritičku vrijednost parametra duljine Le koji za 50% premašuje gornju granicu u standardnom rasponu parametara. U kaotičkom režimu otkriven je naglašeni prozor regularnosti s periodom tri

Overlapped KAM patterns for linearly coupled asymmetric oscillators

The pattern of energy dependence for the onset of chaos is investigated for conservative system of two linearly coupled asymmetric oscillators, harmonic oscillator and a two-well nonlinear oscillator. With increase of energy, the amount of chaoticity first grows up to a certain critical energy, according to the KAM scenario, and above this point, with a further increase of energy, the amount of chaoticity decreases according to the inverse KAM scenario. At the point of transition, there is an overlap of the two scenarios. The position of the critical energy increases with increasing value of the coupling strength between oscillators

Naturally invariant measure of chaotic attractors and the conditionally invariant measure of embedded chaotic repellers

We study local and global correlations between the naturally invariant measure of a chaotic one-dimensional map f and the conditionally invariant measure of the transiently chaotic map f_H. The two maps differ only within a narrow interval H, while the two measures significantly differ within the images f^l(H), where l is smaller than some critical number l_c. We point out two different types of correlations. Typically, the critical number l_c is small. The χ^2 value, which characterizes the global discrepancy between the two measures, typically obeys a power-law dependence on the width ε of the interval H, with the exponent identical to the information dimension. If H is centered on an image of the critical point, then l_c increases indefinitely with the decrease of ε, and the χ^2 value obeys a modulated power-law dependence on ε

Missing preimages for chaotic logistic map with a hole

Chaotic transients and preimages are investigated for a new map proposed recently, having a hole in the unit interval of the r = 4 logistic map. This map is characterized by deviations from Frobenius-Perron equation for average lifetimes in dependence on hole position in the form of bursts of average lifetime. We present classification of these bursts on the basis of average lifetimes. Using time maps it is investigated how these bursts are caused by missing preimages of the hole interval I ^( 0 ). We derive approximate expression for the ratio of lifetimes deduced from Frobenius-Perron and from Kantz-Grassberger equations