This paper establishes the existence of endogenous cycles in infinite-horizon open economy models with a flow collateral constraint. It shows that for plausible parameter configurations, has unique equilibrium exhibiting deterministic which periods debt growth are followed by deleveraging. In particular, three-period exist, implies Li-Yorke Theorem presence any periodicity and chaos. The also a...

In this paper, the dynamics of elementary cellular automaton (ECA) rule 73 is investigated under the framework of the bi-infinite symbolic sequence space. This paper provides a rigorous mathematical analysis for the evolution of symbol sequences in some subsystems of rule 73. ECA rule 73, a member of Wolfram’s class III and Chua’s complex Bernoulli-shift rules, defines many more subsystems with...

This paper studies cellular automata in two aspects: Ergodic and topological behavior. For ergodic aspect, the formulae of measure-theoretic entropy, topological entropy and topological pressure are given in closed forms and Parry measure is demonstrated to be an equilibrium measure for some potential function. For topological aspect, an example is examined to show that the exhibition of snap-b...

Given K real d-by-d nonsingular matrices S 1, . . . , S K , by extending the well-known Li-Yorke chaotic description of a deterministic nonlinear dynamical system, to a discrete-time linear inclusion/control dynamical system xn ∈ {S 1, . . . , S K} xn−1, x0 ∈ R d and n ≥ 1, we study the irregularity of orbit (xn(x0, σ))n≥1, governed by the law σ : N → {1, . . . , K}, for any initial state x0 ∈ ...

This paper is concerned with chaos induced by regular snap-back repellers. One new criterion of chaos induced by strictly coupled-expanding maps in compact sets of metric spaces is established. By employing this criterion, the nondegenerateness assumption in the Marotto theorem established in 1978 is weakened. In addition, it is proved that a regular snap-back repeller and a regular homoclinic ...

The paper analyzes the dynamic properties of the neoclassical one-sector growth model with di!erential savings in the sense of Kaldor}Pasinetti. The economy exhibits unstable steady states and #uctuations if the income distribution varies su$ciently and if shareholders save more than workers. The paper analyzes in detail the dynamics for the case with a "xed proportions technology as well as wi...

Let X be a compact metric space, let φ be a continuous self-map on X , and let F(X) denote the space of fuzzy sets on X equipped with the levelwise topology. In this paper we study relations between various dynamical properties of a given (crisp) dynamical system (X,φ) and its Zadeh’s extension Φ on F(X). Among other things we study various (weak, strong, mild etc.) mixing properties and also s...

In this paper, a mathematical analysis of a possible way to chaos (in the sense of Li and Yorke) for bounded piecewise smooth systems of dimension three submitted to nonsmooth transitions is proposed. This study is based on period doubling method applied to the relied Poincaré map defined on a Poincaré section chosen in the neighborhood of the bifurcation point and transverse to the switching m...

This paper is devoted to an in-depth study of cellular automaton rule 180 under the framework of symbolic dynamics. Rule 180, a member of Wolfram’s class IV and Chua’s hyper Bernoulli shift rules, defines infinite number of generalized sub-shifts. An effective method of constructing the shift invariant sets of the rule’s global map is proposed. It is noted that this method is also applicable to...