Heteroclinic Cycles Imply Chaos and Are Structurally Stable
نویسندگان
چکیده
منابع مشابه
Structurally stable heteroclinic cycles
This paper describes a previously undocumented phenomenon in dynamical systems theory; namely, the occurrence of heteroclinic cycles that are structurally stable within the space of C vector fields equivariant with respect to a symmetry group. In the space X(M) of C vector fields on a manifold M, there is a residual set of vector fields having no trajectories joining saddle points with stable m...
متن کاملStable heteroclinic cycles and symbolic dynamics.
Let S(1) (0), S(1) (1),.,S(1) (n-1) be n circles. A rotation in n circles is a map f: union or logical sum (i=0) (n-1)S(1) (i)--> union or logical sum (i=0) (n-1)S(1) (i) which maps each circle onto another by a rotation. This particular type of interval exchange map arises naturally in bifurcation theory. In this paper we give a full description of the symbolic dynamics associated to such maps.
متن کاملHeteroclinic Cycles and Segregation Distortion
Segregation Distorters are genetic elements that disturb the meiotic segregation of heterozygous genotypes. The corresponding genes are \ultra-sellsh" in that they force their own spreading in the population without contributing positively to the tness of the organisms carrying them. We consider here autosomal two-locus drive systems consisting of a \killer locus" and a \target locus". The dipl...
متن کاملHow structurally stable are global socioeconomic systems?
The stability analysis of socioeconomic systems has been centred on answering whether small perturbations when a system is in a given quantitative state will push the system permanently to a different quantitative state. However, typically the quantitative state of socioeconomic systems is subject to constant change. Therefore, a key stability question that has been under-investigated is how st...
متن کاملMulti–separation, Centrifugality and Centripetality Imply Chaos
Let I be an interval. I need not be compact or bounded. Let f : I → I be a continuous map, and (x0, x1, · · · , xn) be a trajectory of f with xn ≤ x0 < x1 or x1 < x0 ≤ xn. Then there is a point v ∈ I such that min{x0, · · · , xn} < v = f(v) < max{x0, · · · , xn}. A point y ∈ I is called a centripetal point of f relative to v if y < f(y) < v or v < f(y) < y, and y is centrifugal if f(y) < y < v ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Dynamics in Nature and Society
سال: 2021
ISSN: 1607-887X,1026-0226
DOI: 10.1155/2021/6647132