Investigations on the Dynamics of Combination Maps and the Analysis of Bifurcation in a Discontinuous Logistic Map

This thesis is a study of discrete nonlinear systems represented by one dimensional mappings.As one dimensional interative maps represent Poincarre sections of higher dimensional flows,they offer a convenient means to understand the dynamical evolution of many physical systems.It highlighting the basic ideas of deterministic chaos.Qualitative and quantitative measures for the detection and characterization of chaos in nonlinear systems are discussed.Some simple mathematical models exhibiting chaos are presented.The bifurcation scenario and the possible routes to chaos are explained.It present the results of the numerical computational of the Lyapunov exponents (λ) of one dimensional maps.This thesis focuses on the results obtained by our investigations on combinations maps,scaling behaviour of the Lyapunov characteristic exponents of one dimensional maps and the nature of bifurcations in a discontinous logistic map.It gives a review of the major routes to chaos in dissipative systems,namely, Period-doubling ,Intermittency and Crises.This study gives a theoretical understanding of the route to chaos in discontinous systems.A detailed analysis of the dynamics of a discontinous logistic map is carried out, both analytically and numerically ,to understand the route it follows to chaos.The present analysis deals only with the case of the discontinuity parameter applied to the right half of the interval of mapping.A detailed analysis for the n –furcations of various periodicities can be made and a more general theory for the map with discontinuities applied at different positions can be on a similar footing

Nonlinear Dynamics of Nd:YAG lasers: Hopf bifurcation, Multistability and Chaotic Synchronization

In this thesis we have presented some aspects of the nonlinear dynamics of Nd:YAG lasers including synchronization, Hopf bifurcation, chaos control and delay induced multistability.We have chosen diode pumped Nd:YAG laser with intracavity KTP crystal operating with two mode and three mode output as our model system.Different types of orientation for the laser cavity modes were considered to carry out the studies. For laser operating with two mode output we have chosen the modes as having parallel polarization and perpendicular polarization. For laser having three mode output, we have chosen them as two modes polarized parallel to each other while the third mode polarized orthogonal to them.

Hopf bifurcation in parallel polarized Nd:YAG laser

Dynamics of Nd:YAG laser with intracavity KTP crystal operating in two parallel polarized modes is investigated analytically and numerically. System equilibrium points were found out and the stability of each of them was checked using Routh–Hurwitz criteria and also by calculating the eigen values of the Jacobian. It is found that the system possesses three equilibrium points for (Ij, Gj), where j = 1, 2. One of these equilibrium points undergoes Hopf bifurcation in output dynamics as the control parameter is increased. The other two remain unstable throughout the entire region of the parameter space. Our numerical analysis of the Hopf bifurcation phenomena is found to be in good agreement with the analytical results. Nature of energy transfer between the two modes is also studied numerically.

Bifurcation structure and Lyapunov exponents of a modulated logistic map

We have studied the bifurcation structure of the logistic map with a time dependant control parameter. By introducing a specific nonlinear variation for the parameter, we show that the bifurcation structure is modified qualitatively as well as quantitatively from the first bifurcation onwards. We have also computed the two Lyapunov exponents of the system and find that the modulated logistic map is less chaotic compared to the logistic map.

Subcritical Hopf bifurcation in Ne-Nd hollow cathode discharge

We report the experimental observation of subcritical Hopf bifurcation and the existence of non-oscillating “windows” in the dynamics of a Ne-Nd hollow cathode discharge current as the control parameter.

Routing protocol enhancement for handling node mobility in wireless sensor networks

In wireless sensor networks, the routing algorithms currently available assume that the sensor nodes are stationary. Therefore when mobility modulation is applied to the wireless sensor networks, most of the current routing algorithms suffer from performance degradation. The path breaks in mobile wireless networks are due to the movement of mobile nodes, node failure, channel fading and shadowing. It is desirable to deal with dynamic topology changes with optimal effort in terms of resource and channel utilization. As the nodes in wireless sensor medium make use of wireless broadcast to communicate, it is possible to make use of neighboring node information to recover from path failure. Cooperation among the neighboring nodes plays an important role in the context of routing among the mobile nodes. This paper proposes an enhancement to an existing protocol for accommodating node mobility through neighboring node information while keeping the utilization of resources to a minimum.

Performance improvement of multiple Connections in AODV with the concern of Node bandwidth

Mobile Ad-hoc Networks (MANETS) consists of a collection of mobile nodes without having a central coordination. In MANET, node mobility and dynamic topology play an important role in the performance. MANET provide a solution for network connection at anywhere and at any time. The major features of MANET are quick set up, self organization and self maintenance. Routing is a major challenge in MANET due to it’s dynamic topology and high mobility. Several routing algorithms have been developed for routing. This paper studies the AODV protocol and how AODV is performed under multiple connections in the network. Several issues have been identified. The bandwidth is recognized as the prominent factor reducing the performance of the network. This paper gives an improvement of normal AODV for simultaneous multiple connections under the consideration of bandwidth of node.

Routing Protocol Enhancement for handling Node Mobility in Wireless Sensor Networks

In wireless sensor networks, the routing algorithms currently available assume that the sensor nodes are stationary. Therefore when mobility modulation is applied to the wireless sensor networks, most of the current routing algorithms suffer from performance degradation. The path breaks in mobile wireless networks are due to the movement of mobile nodes, node failure, channel fading and shadowing. It is desirable to deal with dynamic topology changes with optimal effort in terms of resource and channel utilization. As the nodes in wireless sensor medium make use of wireless broadcast to communicate, it is possible to make use of neighboring node information to recover from path failure. Cooperation among the neighboring nodes plays an important role in the context of routing among the mobile nodes. This paper proposes an enhancement to an existing protocol for accommodating node mobility through neighboring node information while keeping the utilization of resources to a minimum.

RMAC-M: Extending the R-MAC Protocol for an Energy Efficient, Delay Tolerant Underwater Acoustic Sensor Network application with a mobile data mule node

One of the major applications of underwater acoustic sensor networks (UWASN) is ocean environment monitoring. Employing data mules is an energy efficient way of data collection from the underwater sensor nodes in such a network. A data mule node such as an autonomous underwater vehicle (AUV) periodically visits the stationary nodes to download data. By conserving the power required for data transmission over long distances to a remote data sink, this approach extends the network life time. In this paper we propose a new MAC protocol to support a single mobile data mule node to collect the data sensed by the sensor nodes in periodic runs through the network. In this approach, the nodes need to perform only short distance, single hop transmission to the data mule. The protocol design discussed in this paper is motivated to support such an application. The proposed protocol is a hybrid protocol, which employs a combination of schedule based access among the stationary nodes along with handshake based access to support mobile data mules. The new protocol, RMAC-M is developed as an extension to the energy efficient MAC protocol R-MAC by extending the slot time of R-MAC to include a contention part for a hand shake based data transfer. The mobile node makes use of a beacon to signal its presence to all the nearby nodes, which can then hand-shake with the mobile node for data transfer. Simulation results show that the new protocol provides efficient support for a mobile data mule node while preserving the advantages of R-MAC such as energy efficiency and fairness.

Routing Protocol Enhancement for handling Node Mobility in Wireless Sensor Networks

In wireless sensor networks, the routing algorithms currently available assume that the sensor nodes are stationary. Therefore when mobility modulation is applied to the wireless sensor networks, most of the current routing algorithms suffer from performance degradation. The path breaks in mobile wireless networks are due to the movement of mobile nodes, node failure, channel fading and shadowing. It is desirable to deal with dynamic topology changes with optimal effort in terms of resource and channel utilization. As the nodes in wireless sensor medium make use of wireless broadcast to communicate, it is possible to make use of neighboring node information to recover from path failure. Cooperation among the neighboring nodes plays an important role in the context of routing among the mobile nodes. This paper proposes an enhancement to an existing protocol for accommodating node mobility through neighboring node information while keeping the utilization of resources to a minimum.

Impact of Node Mobility on Routing Protocols for Wireless Sensor Networks

Wireless sensor networks monitor their surrounding environment for the occurrence of some anticipated phenomenon. Most of the research related to sensor networks considers the static deployment of sensor nodes. Mobility of sensor node can be considered as an extra dimension of complexity, which poses interesting and challenging problems. Node mobility is a very important aspect in the design of effective routing algorithm for mobile wireless networks. In this work we intent to present the impact of different mobility models on the performance of the wireless sensor networks. Routing characteristics of various routing protocols for ad-hoc network were studied considering different mobility models. Performance metrics such as end-to-end delay, throughput and routing load were considered and their variations in the case of mobility models like Freeway, RPGM were studied. This work will be useful to figure out the characteristics of routing protocols depending on the mobility patterns of sensors