Noise induced resonance phenomena in coupled map lattices

We analyse different types of resonance phenomena that can occur in a coupled map lattice in the presence of noise with a subthreshold signal. The onsite dynamics considered here is different from previous such studies, namely, a bimodal cubic map capable of bistability in its dynamics. In addition to the resonance observed in the temporal iterates (the conventional stochastic resonance), we establish the possibility of resonance patterns in spatial sequences along the lattice, which we refer to as “Lattice Stochastic Resonance”. The characterising features of both are investigated in detail, under different types of signals with nearest neighbour coupling between lattice points. Possible practical applications are in signal detection, image processing and in communication networks.     

The diamagnetic susceptibilities of succinic acid and succinic anhydride

Proceedings - Mathematical Sciences -     

Stochastic resonance and chaotic resonance in bimodal maps: A case study

We present the results of an extensive numerical study on the phenomenon of stochastic resonance in a bimodal cubic map. Both Gaussian random noise as well as deterministic chaos are used as input to drive the system between the basins. Our main result is that when two identical systems capable of stochastic resonance are coupled, the SNR of either system is enhanced at an optimum coupling strength. Our results may be relevant for the study of stochastic resonance in biological systems.     

Critical exponents in the transition to chaos in one-dimensional discrete systems

We report the numerically evaluated critical exponents associated with the scaling of generalized fractal dimensions during the transition from order to chaos. The analysis is carried out in detail in the context of unimodal and bimodal maps representing typical one-dimensional discrete dynamical systems. The behavior of Lyapunov exponents (LE) in the cross over region is also studied for a complete characterization.     

Synthesis and morphological change in poly(ethylene oxide)-sodium chlorate based polymer electrolyte complex with polyaniline

The composites of polyethylene oxide:polyaniline:sodium chlorate is prepared by stirring with anhydrous acetonitrile for 5-6 h to form homogeneous solutions/gels at different weight percentages. The composites are characterized by FTIR and SEM. The predominant peaks that appeared in FTIR spectra confirm the formation of PEO:PANI:NaClO₄ composites. It is found from the SEM studies that there is a significant change in the morphology of various weight percentages of NaClO₄ in PEO-PANI matrix, i.e. from ellipsoidal to square. DC conductivity behavior is seen due to hopping of polarons from one localized state to another that can be confirmed by Mott theory. It is observed from the DC conductivity and SEM studies that these composites can be promising candidates for solid state electrolytes.     

Activity-guided isolation of antioxidant xanthones from Swertia chirayita (Roxb.) H. Karsten (Gentianaceae)

An activity-guided isolation and purification process was used to identify the DPPH (l,l-diphenyl-2-picrylhydrazyl) radical-scavenging components of Swertia chirayita. A dry, whole plant of S. chirayita was extracted with different solvents and tested for its DPPH radical-scavenging activity. The acetone?:?water (8?:?2) extract showed the highest total phenolic content (TPC) and DPPH radical-scavenging activity, which was column chromatographed to obtain decussatin, swertianin, bellidifolin, isobellidifolin, amarogentin, swertianolin and mangiferin as active components. Good correlation was observed between TPC and DPPH scavenging activity among the extracts. The unique structure of xanthones, including the catecholic moiety and the completely conjugated system, enables them to be promising antioxidants.     

Transition to chaos in a driven pendulum with nonlinear dissipation

The Melnikov-Holmes method is used to study the onset of chaos in a driven pendulum with nonlinear dissipation. Detailed numerical studies reveal many interesting features like a chaotic attractor at low frequencies, band formation near escape from the potential well and a sequence of subharmonic bifurcations inside the band that accumulates at the homoclinic bifurcation point.     

Stability condition for functional equation through fixed point in the large

Stability and asymptotic stability conditions for the solution of functional equation of the formφ(x)=f(x)+g(x)φ[α(x)] through the method of fixed point in the large has been investigated.