Volume 5 (2015)  

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1.  An Averaging Result for Fuzzy Differential Equations with a Small Parameter  Full text (PDF)

Amel Bourada, Rahma Guen and Mustapha Lakrib

Pages: 1-9

Abstract:  For fuzzy differential equations with a small parameter we prove an aver-aging result on finite time intervals and under rather weak conditions.

2. Evolution of Chaotic Domain in the Discrete Lotka-Volterra Model for Predator-Prey Interaction

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P. P. Saratchandran,, K. C. Ajithprasad and  K. P. Harikrishnan

Pages: 10-32

Abstract:  We undertake a detailed numerical analysis of the discrete version of the Lotka-Volterra model for predator-prey interactions. A complete picture of the long time dynamics of the system is presented including the type of bifurcations, nature of the underlying attractors and the general pattern for the transition to chaos, as each of the control parameter is varied independently. We are able to identify how the domain of chaos evolves in the parameter plane with the help of a dimensional analysis using a recently proposed algorithmic scheme for computing the fractal dimension of a chaotic attractor from time series. Finally, we also report the presence of a small region in the parameter plane with fractal structure where, the asymptotic dynamics depends sensitively on the control parameter values.

3. True and False Chaotic Attractors in a 3-D Lorenz-type System  Full text (PDF)

Haijun Wang and Xianyi Li 

Pages: 33-41

Abstract:  In some known literatures those authors have analyzed the Yang system, x'=a(y-x), y'=cx-xz, z'=-bz+xy, containing three independent parameters. They think that they have found the system to have two interesting chaotic attractors (called as Yang-Chen attractor) when (a,b,c)=(10,8/3,16) and (a,b,c)=(35,3,35), respectively. However, by further analysis and Matlab simulation, we show that the two Yang--Chen chaotic attractors found are actually pseudo ones. In fact, the two attractors are locally asymptotically stable equilibria. Further, we present the values of parameters for this system to really generate chaotic attractor. Accordingly, we find a new attractor in the Yang system co-existing with one saddle and two stable node-foci.