[PDF] Top 20 Escape from a chaotic attractor with fractal basin boundaries

... probable escape path (MPEP) from the CA that approaches an accessible orbit on the fractal ...of escape paths inside the fractal basin is briefly ... See full document

... stems from the complexity of the system dynamics near a CA and in general near boundaries, which may be ...with fractal basin ...6] from the microscopic to the macroscopic equations of ... See full document

... of chaotic flows and maps, there exists a unique most probable path along which the system escapes from the basin of attraction of a chaotic ...for escape over both regular and ... See full document

... noise-induced escape from a chaotic attractor 1]. Chaotic systems are widespread in nature, and the study of their dynamics in the presence of uctuations is both of fundamen- tal ... See full document

... The prehistory of escape from the Lorenz attractor is defined by stable and unstable manifolds of the saddle center point, and the escape itself consists of crossing the saddle cycle sur[r] ... See full document

... needed from Hamiltonian fluctuation theory are introduced and it is shown for a given model that the Hamiltonian systems arising in the analysis of both the problem of fluctuational escape and the prob- lem ... See full document

... optimal escape path, we use exactly the same technique as in the case of the LD FBB, ...seen from this figure, the system (4) leaves the stable point O at the origin along the unique optimal escape ... See full document

... that escape takes place at an accessible point on the basin boundary, and the procedures used for minimization of the activation en- ergy are ...noise-induced escape from a periodic ... See full document

... with chaotic behaviour [1,2] including e.g. a demonstration of chaotic features in a purely stochastic Kramers oscillator [3], the phenomena of both noise-induced instability [4] and noise-induced order ... See full document

... noise-induced escape from a non-hyperbolic [18] chaotic attractor in a non-autonomous nonlinear oscillator [10, ...noise-induced escape from a quasi-hyperbolic [18] ... See full document

... transition from stable two-dimensional to fully three-dimensional ...vertical boundaries and idealised boundary conditions on horizontal ...change from a chaotically varying two-dimensional ow (with ... See full document

... stretch from the smallest copy with dilatation factors,  = 1, 2, 4, ...Therefore, from 3 variables, statements about uniqueness and asymptotic stability can be generalized to n-1 dimen- ... See full document

... of fractal dimensional global attractor and, moreover, the dynamics of the global attrac- tor converges to that of the well known Cagilnap phase-field ... See full document

... u − ∆ + β u α u − φ ∇ u ∆ + u g u = f x . (4) They obtained the exponential attractors and inertial manifolds for above equ- ation. In addition, Yunlong Gao et al. also made their own contribution to the research of the ... See full document

... attraator used to describe these attractors on which the motion appeared chaotic, was coined by Ruelle and Takens, who independently proposed strange attractor behaviour as a model of fl[r] ... See full document

... between fractal dimension and burial depth (Figure 6d). The fractal dimension of pore has a weakly positive correlation with ...the fractal dimension presents an increasing trend with the increase of ... See full document

... Particle swarm optimization algorithm (Particle Swarm Optimization), referred to as PSO, is a newly developed evolutionary algorithm, and its thought originated from birds, fish and other groups foraging behavior. ... See full document

... We have demonstrated thus far that the Trojan Y Chromosome model is well posed. We have also shown there exists a global attractor for the system. This validate the TYC strategy as an effective means of eradication ... See full document

... The formula for the quantum amplitude of the Veneziano dual resonance model is shown to be formally analogous to the dimensionality of a K-theoretical fractal quotient manifold of the non-commutative geometrical ... See full document

... DOI: 10.4236/jamp.2017.512197 2413 Journal of Applied Mathematics and Physics attractors and the existence of a fractal exponential attractor with non-supercritical and critical cases by Guoguang Lin and ... See full document