We explore different two parametric families of quasi-periodically Forced Logistic Maps looking for universality and self-similarity properties. In the bifurcation diagram of the one-dimensional Logistic Map it is well known that there exist parameter values sn where the 2-periodic orbit is superattracting. Moreover, these parameter values lay between the parameters corresponding to two consecu...

The nature of the round-off errors that occur in the usual double precision computation of the logistic map is studied in detail. Different iterative regimes from the whole panoply of behaviors exhibited in the bifurcation diagram are examined, histograms of errors in trajectories given, and for the case of fully developed chaos an explicit formula is found. It is shown that the statistics of t...

In order to make better agreement with transonic wind tunnel experimental data, which was obtained in the Japan Aerospace Exploration Agency (JAXA) in 1990’s, we proposed new mathematical model to improve the previous model. The bifurcation diagram was analyzed by a continuation method. The continuation method can continuously follow the solutions of dynamical system, such as a limit cycle osci...

Models describing microscopic or mesoscopic phenomena in physics are inherently discrete, where the lattice spacing between fundamental components, such as in the case of atomic sites, is a fundamental physical parameter. The effect of spatial discreteness over front propagation phenomenon in an overdamped one-dimensional periodic lattice is studied. We show here that the study of front propaga...

A detailed mathematical analysis is performed to understand the anode potential oscillations observed experimentally in a proton exchange membrane fuel cell ~PEMFC! with H2 /CO feed ~Ref. 9!. Temperature and anode flow rate are found to be key bifurcation parameters. The time dependence of all the key surface species must be accounted for in order for the model to predict the oscillatory behavi...

A stability analysis is presented of the hydrolysis of methyl isocyanate (MIC) using a homogeneous flow reactor paradigm. The results simulate the thermal runaway that occurred inside the storage tank of MIC at the Bhopal Union Carbide plant in December 1984. The stability properties of the model indicate that the thermal runaway may have been due to a large amplitude, hard thermal oscillation ...

In this work we consider the problem of classifying all configurations of singularities, both finite and infinite of quadratic differential systems, with respect to the geometric equivalence relation defined in [2]. This relation is finer than the topological equivalence relation which does not distinguish between a focus and a node or between a strong and a weak focus or between foci (or saddl...

Abstract. This article attempts to analyze the Hopf bifurcation behavior of a railway wheelset in the presence of dead-zone and yaw damper nonlinearities. A model that is more precise than Yang and Ahmadian is investigated. Using Bogoliubov-Mitropolsky averaging method and critical speed, the amplitude of the limit cycle in the presence of the mentioned nonlinearities is taken into consideratio...

The continuous Bonhoeffer–van der Pol (BVP for short) oscillator is transformed into a mapbased BVP model by using the forward Euler scheme. At first, the bifurcations and chaos of the map-based BVP model are investigated when the step size varies as a bifurcation parameter. By using the fast-slow decomposition technique, a two-parameter bifurcation diagram is obtained to give insight into the ...