an averaging model for chaotic system with periodic time varying parameter in this paper we provide a mathematical justification to explain the dynamics of chaotic system with periodic time varying parameter which have been illustrated by some of us in a previous paper 1 based on an equivalent averaging model it is proved that such a parametric time varying system follows the same trajectory of its averaging model provided that the parameter is varied periodically with a sufficiently high frequency some other observations related with this class of chaotic systems are also remarked in this paper

shape and morse theory of attractors we study the shape in the sense of borsuk of attractors of continuous semi dynamical systems on general metric spaces we show in particular that the natural inclusion of the global attractor into the state space is a shape equivalence this and other results of the paper are used to develop an elementary morse theory of an attractor 2000 john wiley sons inc

existence theorems for solutions to random fuzzy differential equations abstract we examine a random fuzzy initial value problem with two kinds of fuzzy derivatives for both cases we establish the results of existence and uniqueness of local solutions to random fuzzy differential equations the existence of global solutions is also obtained

topological properties of the spaces of regular fuzzy sets abstract by identifying the space f 0 x of regular fuzzy sets with a subspace t 0 x of some compact set valued function space we define a uniform topology on f 0 x and discuss several topological properties such as first countability separability connectedness etc when x is a reflexive banach space f 0 x is imbedded into a locally convex topological vector space and a definition of integration and differentiation for f 0 x valued functions is given

on random fuzzy differential equations we consider a cauchy problem in a random fuzzy setting under the condition of lipschitzean right hand side the existence and uniqueness of the solution is proven also the continuous dependence on the right hand side and initial condition is shown some kind of boundedness of the solution is established

attractors synthesis for a lotka volterra like system the aim of this paper is to prove numerically via computer graphic simulations that the synthesis algorithmprovided by danca et al 1 can be utilized to synthesize any attractor of a dynamical system modeling a two predator one prey lotka volterra like system the algorithm switches in a periodic deterministic or a random way the control parameter inside a set of a chosen values the obtained attractor is the same with the attractor obtained for parameter value taken as averaged value of the switched control values this simple and effective algorithm relies on a convex property induced in the set of the attractors corresponding to the chosen switching parameters the algorithm was tested successfully on systems depending linearly on the control parameter like lorenz chen rossler networks and other systems

parameter switching synchronization abstract in this paper we show how the parameter switching algorithm utilized initially to approximate attractors of a general class of nonlinear dynamical systems can be utilized also as a synchronization induced method two illustrative examples are considered the lorenz system and the rabinovich fabrikant system

numerical solutions of fuzzy differential equations abstract numerical algorithms for solving fuzzy ordinary differential equations fode are considered a scheme based on the classical euler method is discussed in detail and this is followed by a complete error analysis the algorithm is illustrated by solving several linear and nonlinear fuzzy cauchy problems

on the topological equivalence of some fuzzy flows near hyperbolic equilibria the purpose of this work is to study fuzzy dynamical systems associated with deterministic systems the grobman hartman theorem states that near hyperbolic equilibria there exists a homeomorphism between the nonlinear system s trajectories and the linearized correspondent system s trajectories that is these systems are topologically equivalent a theorem similar to grobman hartman theorem to fuzzy flows is the main result in this article for fuzzy flows obtained from each system it states that the nonlinear and the linearized are topologically equivalent

a switching scheme for synthesizing attractors of dissipative chaotic systems in this paper a periodic parameter switching scheme is proposed for synthesizing a large class of hyperbolic attractors of continuous time and autonomous dissipative chaotic systems depending linearly on a single real bifurcation parameter it is illustrated by numerical simulations that a wide range of hyperbolic attractors can be obtained by this new scheme the scheme can also be considered as an effective way for control and anticontrol of chaos

adaptive variable structure control for chaos suppression of unified chaotic systems this paper investigates the chaos suppression problem for a class of unified chaotic systems subject to uncertainties and control input with dead zone nonlinearity using the variable structure control technique a robust adaptive control law is established to suppress chaos in a class of unified chaotic systems even with unknown uncertainties and dead zone nonlinearity in input in particular a switching surface is newly proposed to simplify the task of ensuring the stability of the closed loop system in the sliding mode numerical results validate the effectiveness of the proposed adaptive control scheme

fuzzy laplace transform based on the henstock integral and its applications in discontinuous fuzzy systems abstract the existing results on the fuzzy laplace transform and their applications were based on zaheh s decomposition theorem and were formally characterized by the integrals of real valued functions directly that is the existence of the fuzzy laplace transform in essence has not been solved in this article the fuzzy laplace transform is incorporated into the framework of the henstock integral and proposed by use of fuzzy henstock integrals on infinite intervals in addition as a theoretical basis the existence and the basic properties of the fuzzy laplace transform are investigated the convolution of fuzzy valued functions and real valued functions is defined and the convolution theorem of the fuzzy laplace transform is given finally discontinuous fuzzy initial value problems and two kinds of fuzzy volterra integral equations are discussed with use of the fuzzy laplace transform presented in this article

branched surfaces and attractors i dynamic branched surfaces we show how using ideas of r f williams about branched sur faces hyperbolic attractors of flows on three manifolds may be classified up to topological equivalence on an isolating neighborhood by a finite combinatorial object a swaddled graph

can two chaotic systems give rise to order abstract the recently discovered parrondo s paradox claims that two losing games can result under random or periodic alternation of their dynamics in a winning game losing losing winning in this paper we follow parrondo s philosophy of combining different dynamics and we apply it to the case of one dimensional quadratic maps we prove that the periodic mixing of two chaotic dynamics originates an ordered dynamics in certain cases this provides an explicit example theoretically and numerically tested of a different parrondian paradoxical phenomenon chaos chaos order

dynamics and bifurcations of fuzzy nonlinear dynamical systems this article presents a study on how changes in fuzzy parameters can affect the behavior of fuzzy solutions such fuzzy solutions are obtained by applying the zadeh extension principle on deterministic solutions of autonomous differential equations we define the concepts of topological equivalence and fuzzy bifurcation value for fuzzy flows using these notions we prove some results for the existence of such bifurcation values we also provide some examples and computational simulations to illustrate the results

numerical solutions of fuzzy differential and integral equations using the embedding method numerical procedures for solving fuzzy differential equations fdes and fuzzy integral equations fies with arbitrary kernels have been investigated sufficient conditions for convergence of the proposed algorithms are given and their applicability is illustrated with examples this work and its conclusions may narrow the gap between the theoretical research on fdes and fies and the practical applications already existing in the design of various fuzzy dynamical systems

deterministic and random synthesis of discrete chaos in this paper two anticontrol algorithms for synthesis of discrete chaos are introduced in these algorithms the control parameter of a discrete dynamical system is switched either randomly or in a deterministic way between two or more values corresponding to periodic motions the result being chaotic behavior these algorithms require no knowledge of specific mathematical properties of the underlying map modeling the system the existence of chaos is demonstrated using various tools including graphical iteration histogram lyapunov exponent and surrogate tests in this paper these very simple and implementable chaotifiers are applied to the logistic map

parameter switching in a generalized duffing system finding the stable attractors this paper presents a simple periodic parameter switching method which can find any stable limit cycle that can be numerically approximated in a generalized duffing system in this method the initial value problem of the system is numerically integrated and the control parameter is switched periodically within a chosen set of parameter values the resulted attractor matches with the attractor obtained by using the average of the switched values the accurate match is verified by phase plots and hausdorff distance measure in extensive simulations

asymptotic behavior of solutions of fuzzy differential equations abstract we study the asymptotic behaviour of the solutions of the fuzzy differential equations the method of successive approximation is used to establish our results

meshless local b spline fd method and its application for 2d heat conduction problems with spatially varying thermal conductivity abstract in this paper a new class of meshless methods based on local collocation and b spline basis functions is presented for solving elliptic problems the proposed approach is called as meshless local b spline basis functions based finite difference local b fd method the method was straightforward to develop and program as it was truly meshless only scattered nodal distribution was required hence avoiding at all mesh connectivity for field variable approximation and integration in the method any governing equations were discretized by b spline approximation in the spirit of fd technique using local b spline collocation i e any derivative at a point or node was stated as neighboring nodal values based on the b spline interpolants in addition as b spline basis functions pose favorable properties such as i easy to construct to any arbitrary order degree ii have partition of unity property and iii can be easily designed to pose the kronecker delta property the shape function construction as well as the imposition of boundary conditions can be incorporated efficiently in the present method the applicability and capability of the present local b fd method were demonstrated through several heat conduction problems with heat generation and spatially varying conductivity

existence of the solutions of fuzzy differential equations with parameters in this paper we study the existence of the solutions of fuzzy differential equations with parameters by the topological degree method

on the concept of attractor this note proposes a definition for the concept of attractor based on the probable asymptotic behavior of orbits the definition is sufficiently broad so that every smooth compact dynamical system has at least one attractor