chaos theory discusses unstable and non-periodic behavior of non-linear fluctuating dynamicsystems. since evaporation level variations of lakes have a dynamic identity, chaos theory can have a uniquerole in collecting data of these variations. therefore it is an important and challenging problem in the field ofplanning and qualitative and quantitative management of urmia lake to verify whether ...

A multicriteria recommendation algorithm for tourist routes under the multidimensional expanded spatial grid structure model based on fuzzy C-means clustering of preferences is proposed. The purpose proposed to improve intelligent ability popular core circle. enlarged well-known circle used develop correlation travel restricted sample training. Under traveler circle’s framework, mixed kernel us...

Strange nonchaotic attractors (SNA) arise in quasiperiodically driven systems in the neighborhood of a saddle node bifurcation whereby a strange attractor is replaced by a periodic (torus) attractor. This transition is accompanied by Type-I intermittency. The largest nontrivial Lyapunov exponent Λ is a good order–parameter for this route from chaos to SNA to periodic motion: the signature is di...

We propose using discrete dynamical systems to model non-Markovian processes. This implies a whole hierarchy of dynamical systems with dimensionality increasing proportional to the memory. Specific long-range memory effects are investigated for a quadratic, a cubic and a quartic map. Markovian processes transform the quadratic map into a normal form of the logistic equation; the H6non map corre...

This chapter deals with bifurcation dynamics in control systems, which are described by ordinary differential equations, partial differential equations and delayed differential equations. In particular, bifurcations related to double Hopf, combination of double zero and Hopf, and chaos are studied in detail. Center manifold theory and normal form theory are applied to simplify the analysis. Exp...

We investigate the nonlinear properties of a system introduced by Burridge and Knopoff to model the dynamics of earthquakes. We find that a two-block system in a completely homogeneous configuration presents a complex behavior characterized by the presence of periodic, quasiperiodic and chaotic orbits. We have found routes to chaos via two types of intermittencies and period doubling bifurcatio...

Renormalization group has become a standard tool for describing universal properties of different routes to chaos – period-doubling in unimodal maps, quasiperiodic transitions in circle maps, dynamics on the boundaries of Siegel disks, destruction of invariant circles of area-preserving twist maps, and others. The universal scaling exponents for each route are related to the properties of the c...

We study the ta( tonnement process in an exchange economy with three commodities and three agents. We argue that for the multiplicative ta( tonnement process the simplex is a natural normalization rule. We analyse the in#uence of symmetry in preferences and endowments on the dynamics of the ta( tonnement process. Depending on this symmetry there are di!erent bifurcation routes to chaos. In part...

This paper is concerned with the study of third order quadratic and autonomous systems and the interest is oriented to the stable periodic oscillations. From the “jerk” equation model, the classes of minimal complexity presenting a Hopf bifurcation are derived and their local characterization is carried out by means of a suitable harmonic balance technique. Other possible system reductions pres...