Moiseis dos Santos Cecconello

On the stability of fuzzy dynamical systems

Abstract In this work we study the asymptotic behavior of fuzzy solutions obtained by using Zadehs extension at the deterministic solutions of initial value problems. We obtain some result regarding the existence of fuzzy equilibrium points that generalize the already known results. As show earlier, the membership function of the fuzzy equilibrium points may be obtained in a relatively simple way. Also, we study the projection of the fuzzy solution on the appropriate subspaces of the phase space. Several examples are given to illustrate the obtained results.

Periodic orbits for fuzzy flows

Abstract Periodic solutions are present in many of the various mathematical models that describe physical, chemical or biological phenomena. In this work we investigate the existence of periodic solutions for fuzzy initial value problem. We will show that fuzzy solutions can present periodic points and we will develop tools of qualitative analysis for such solutions. Some models are presented to illustrate the results obtained in this paper.

Stationary Points—I: One-Dimensional p-Fuzzy Dynamical Systems

p-Fuzzy dynamical systems are variational systems whose dynamic is obtained by means of a Mamdani type fuzzy rule-based system. In this paper, we will show the 1-dimensional p-fuzzy dynamical systems and will present theorems that establish conditions of existence and uniqueness of stationary points. Besides the obtained analytical results, we will present examples that illustrate and confirm the obtained mathematical results.

Invariant and attractor sets for fuzzy dynamical systems

Abstract In this work we establish conditions for the existence and stability of invariant sets for dynamical systems defined on metric space of fuzzy subsets of R n . We show that the results presented in this work generalize some conditions of existence and stability of equilibrium points and periodicity of fuzzy differential equations solutions.

About Projections of Solutions for Fuzzy Differential Equations

In this paper we propose the concept of fuzzy projections on subspaces of , obtained from Zadehs extension of canonical projections in , and we study some of the main properties of such projections. Furthermore, we will review some properties of fuzzy projection solution of fuzzy differential equations. As we will see, the concept of fuzzy projection can be interesting for the graphical representation of fuzzy solutions.

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.

On fuzzy uncertainties on the logistic equation

Abstract It is recognized that handling uncertainty is essential to obtain more reliable results in modeling and computer simulation. This paper aims to discuss the logistic equation subject to fuzzy uncertainties in the initial conditions and parameters. Here we consider the population density at a specific time as a fuzzy variable in which the possibility distribution function depends on the possibility distribution functions of the environmental carrying capacity, the initial population density and the intrinsic growth rate. We provide closed-form expressions for the expected value of the fuzzy variables population density and for the time of maximum growth. We also perform some numerical simulations to illustrate our main results.

P-Fuzzy Diffusion Equation Using Rules Base

We propose a fuzzy system that simulates dispersion of individuals whose movements are described by diffusion. We will use only the position of the population as an input variable for describing the process. We emphasize that the classical diffusion equation along with its analytical solution in no time was used for obtaining our solution.

Prey-Predator Model Under Fuzzy Uncertanties

This work studies the influence of fuzzy uncertainties on the asymptotic behavior of the solution of a prey-predator model. Here, initial conditions and parameters are interpreted as fuzzy variable. The population densities at a specific time are also interpreted as a fuzzy variable in which the possibility distribution function depends on the possibility distribution functions of the parameters. We provide closed formulas for expected values of some equilibrium points. We also compare the expected value of the fuzzy solution with the deterministic solution providing computational simulations in order see the difference between theses approaches.

Bifurcations of fuzzy solutions

In this work we study the dynamics of bifurcations of fuzzy solutions with parameters and/or initial condition dependencies by applying the Zadehs extension to the deterministic solution. We define the concept of “fuzzy bifurcation value”, by qualitative changes of stability equilibrium solutions. Using these changes we obtain some results on the existence of such bifurcation values. We also provide some illustrative examples and computational simulations illustrating the asymptotic behavior.