this paper investigates the dynamics and stability properties of a discrete-time lotka-volterra type system. we first analyze stability of the fixed points and the existence of local bifurcations. our analysis shows the presence of rich variety of local bifurcations, namely, stable fixed points; in which population numbers remain constant, periodic cycles; in which population numbers oscillate amo...

We demonstrate that the dynamics toward and within the Feigenbaum attractor combine to form a q -deformed statistical-mechanical construction. The rate at which ensemble trajectories converge to the attractor (and to the repellor) is described by a q entropy obtained from a partition function generated by summing distances between neighboring positions of the attractor. The values of the q indi...

AbstructA dc-dc buck converter controlled by naturallysampled, constant-frequency pulsewidth modulation in continuous conduction mode gives rise to a great variety of behavior, depending on the values of the parameters of the circuit. We analyze the one-periodic and two-periodic orbits which cross the voltage ramp once per cycle, and we study their stability by computing the characteristic mult...

We discuss one parameter families of unimodal maps, with negative Schwarzian derivative, unfolding a saddle-node bifurcation. We show that there is a parameter set of positive but not full Lebesgue density at the bifurcation, for which the maps exhibit absolutely continuous invariant measures which are supported on the largest possible interval. We prove that these measures converge weakly to a...

Periodic and quasi-periodic orbits are important objects that explain much of the dynamics in several Hamiltonian models in Celestial Mechanics. Adding a friction proportional to the velocity of the particles , an increasingly common asumption in Celestial Mechanics, gives rise to conformally symplectic models. Greene's criterion for twist mappings asserts the existence of a KAM torus by examin...

In this paper, we analyze the algebraic structure of some null boundary as well as some periodic boundary 2-D Cellular Automata (CA) rules by introducing a new matrix multiplication operation using only AND, OR instead of most commonly used AND, EX-OR. This class includes any CA whose rule, when written as an algebra, is a finite Abelean cyclic group in case of periodic boundary and a finite co...

By constructing suitable Lyapunov functions, we study the existence, uniqueness and global exponential stability of periodic solution for impulsive Hopfield neural networks with time-varying delays. Our condition extends and generalizes a known condition for the global exponential periodicity of continuous Hopfield neural networks with time-varying delays. Further the numerical simulation shows...

The authors investigate the impact of external sources on the pattern formation of concentration profiles of passive tracers in a twodimensional shear flow. By using the pullback attractor technique for the associated nonautonomous dynamical system, it is shown that a unique time-almost periodic concentration profile exists for timealmost periodic external source. ∗This work was partly supporte...

A delay in feedback can stabilize simultaneously several unstable periodic orbits embedded in a chaotic attractor. We show that by modulating the feedback variable it is possible to lock one of these states and eliminate other coexisting periodic attractors. The method is demonstrated with both a logistic map and a CO2 laser model.  2003 Elsevier B.V. All rights reserved. PACS: 05.45.Ac; 05.45...

A new 3D autonomous dynamical system proposed by Dequan Li [Physics Letters A, 372, 387, 2008.] produces a chaotic attractor whose global topological properties are unusual. The attractor has a rotation symmetry and only a single real fixed point for the parameters used in his study. The symmetric, complex pair of fixed points cannot be ignored: they play a major role in organizing the motion o...