Sunita Gakkhar

Chaos in seasonally perturbed ratio-dependent prey–predator system

Abstract We investigate the effects of periodic forcing, in the intrinsic growth rate of the prey, on the Holling–Tanner ratio-dependent prey–predator system. Lyapunov exponents, Lyapunov dimension, and Poincare section are obtained for section of parametric space for the resulting forced system. The abundance of steady state chaotic solutions is detected when seasonality is super imposed on the system, which otherwise has a globally stable equilibrium state or globally stable limit cycle. The results support the conjecture that seasons can very easily give rise to complex population dynamics.

Order and chaos in predator to prey ratio-dependent food chain

Abstract In this article, we investigate the dynamical behavior and chaos of a realistic three species food chain model considering predator to prey ratio-dependence for the interaction together with type II functional response. The model, for biologically reasonable parameter values, exhibits stable, periodic and chaotic dynamics in long-time behavior. The bifurcation diagrams have been obtained; Lyapunov exponents and dimensions have been computed. The model shows the rich dynamics in the positive octant. The dynamics behavior is found to be very sensitive to parameter values and initial data.

Chaos in three species ratio dependent food chain

Abstract Three species ratio dependent food chain model is considered. To study the global dynamic behavior of the resulting nonlinear coupled system, it is solved numerically for large values of time. The biological parameters are varied to investigate the irregularity in the patterns and existence of chaos. The chaotic attractor is obtained for suitable choice of parametric values.

Existence of chaos in two-prey, one-predator system

Abstract A two-prey, one-predator model incorporating nonlinear functional response is investigated analytically as well as numerically. The system appears to exhibit chaos for a range of parametric values when long time behavior studied.

Order and chaos in a food web consisting of a predator and two independent preys

Abstract A food web consisting of two independent preys and a predator is modeled incorporating modified Holling type-II functional response. The mathematical model has a unique and bounded solution. The necessary and sufficient conditions for persistence of the food web are obtained. Bifurcation diagram has been obtained for selected range of different parameters. The system exhibits chaos for a range of parametric values when long time behavior is studied. The computation of Lyapunov exponents and the existence of strange attractor also indicate the chaotic behavior of the system.

Seasonally perturbed prey–predator system with predator-dependent functional response

Abstract The effect of seasonality on the prey–predator model with predator-dependent trophic function is investigated analytically as well as numerically. The effect of periodic variations is considered on two different parameters of the system: the growth rate of prey and the death rate of the predators. The two parameters may not be in the same phase. The behavior of the system is simulated and bifurcation diagrams are obtained for different parameters. The results show that seasonality in two different parameters with or without phase difference can give rise to multiple attractors, including chaos, with variations in critical parameters.

Dynamical behavior of two predators competing over a single prey

Dynamical behavior of a food web comprising two predators competing over a single prey has been investigated. The analysis of the food web model shows that the persistence is not possible for two competing predators sharing a single prey species in the cases when any one of the boundary prey-predator planes has a stable equilibrium point. The principle of competitive exclusion holds in such cases. However, numerical simulations exhibit persistence in the presence of periodic solutions in the boundary planes. The system exhibits quasi-periodic behavior in the positive octant. The co-existence in the form of a limit cycle is also possible in some cases.

A mathematical model for viral infection in toxin producing phytoplankton and zooplankton system

In this paper, we investigate the dynamical behaviour of toxin producing phytoplankton (TPP) and zooplankton. The phytoplanktons are divided into two groups, namely susceptible phytoplankton and infected phytoplankton. The conditions for coexistence for the populations are presented. In this model, we are discussing the effect of toxin substance. The system exhibits periodic oscillations in small region for rate of infection parameter and rate of toxin liberation parameter. For the higher values of rate of infection, it shows the quasi-periodic behaviour, which is responsible for bloom.

HORI: a web server to compute Higher Order Residue Interactions in protein structures

BackgroundFolding of a protein into its three dimensional structure is influenced by both local and global interactions within a protein. Higher order residue interactions, like pairwise, triplet and quadruplet ones, play a vital role in attaining the stable conformation of the protein structure. It is generally agreed that higher order interactions make significant contribution to the potential energy landscape of folded proteins and therefore it is important to identify them to estimate their contributions to overall stability of a protein structure.ResultsWe developed HORI [Higher order residue interactions in proteins], a web server for the calculation of global and local higher order interactions in protein structures. The basic algorithm of HORI is designed based on the classical concept of four-body nearest-neighbour propensities of amino-acid residues. It has been proved that higher order residue interactions up to the level of quadruple interactions plays a major role in the three-dimensional structure of proteins and is an important feature that can be used in protein structure analysis.ConclusionHORI server will be a useful resource for the structural bioinformatics community to perform analysis on protein structures based on higher order residue interactions. HORI server is a highly interactive web server designed in three modules that enables the user to analyse higher order residue interactions in protein structures. HORI server is available from the URL: http://caps.ncbs.res.in/hori

Computational prediction and analysis of impact of the cross-talks between JNK and P38 kinase cascades.

Signal transduction is a complex protein signaling process with a rich network of multifunctional interactions that occur in a non‐linear fashion. Mitogen‐activated protein kinase (MAPK) signal transduction pathways regulate diverse cellular processes ranging from proliferation and differentiation to apoptosis. In mammals, out of five, there are three well characterized subfamilies of MAPKs ‐ ERKs (Extracellular signal‐regulated kinases), JNKs (c‐Jun N‐terminal kinases), and P38 kinases, and their activators, are implicated in human diseases and are targets for drug development. Kinase cascades in MAPK pathways mediate the sensing and processing of stimuli. To understand how cells makes decisions, the dynamic interactions of components of signaling cascades are important rather than just creating static maps. Based on enzyme kinetic reactions, we have developed a mathematical model to analyze the impact of the cross‐talks between JNK and P38 kinase cascades. Cross‐talks between JNK and P38 kinase cascades influence the activities of P38 kinases. Responses of the signals should be studied for network of kinase cascades by considering cross‐talks.