No abstract

Chaos in Shimizu-Morioka system is controlled by applying a Lie algebraic exact linearization technique. In this state space exact linearization method, a non-linear feedback control law is designed which induces a coordinate transformation thereby changing the original non-linear chaotic system into a linear controllable one. The controller is designed for an arbitrary output and the paper discusses the case of both linear and non-linear outputs. Necessary and sufficient conditions are derived for stabilization of the system to a point and onto a limit cycle. Numerical simulation has been conducted for all these aspects of the problem that conclusively establishes our analytical findings.

This paper investigates the synchronization rate for identical synchronization of chaotic dynamical systems, achieved by using controllers. The paper stresses on the hybrid feedback control technique and the tracking control technique and determines their corresponding maximum, minimum, and average synchronization rates. The results obtained are applied on the Shimizu-Morioka chaotic system, and some necessary and sufficient conditions for synchronization are obtained. Comparison of the two controllers is undertaken on the basis of their synchronization rates, in the context of the Shimizu-Morioka system. The results are analyzed both theoretically and numerically. Moreover, a method of graphical analysis is proposed to completely characterize the set of hybrid controllers for a given system.

Modern day agriculture is dependent on the use of chemical agents for maximizing crop yield. This practice has perilous effects on the ecosystem if used in an unchecked manner. The present paper develops a mathematical model of an agricultural system that incorporates the cumulative effect of the chemical agents like pesticides, fertilizers etc. Dynamical behaviour of the system, such as boundedness, permanence and stability, are studied. Numerical simulations are carried out to study the changes in the behaviour of the system due to varying levels of potency of the chemicals. Based on these, an effort is made to determine the conditions necessary for a sustainable and productive agricultural system in presence of chemical agents. Applicability of the model in related scenarios is also discussed.

At the core of understanding dynamical systems is the ability to maintain and control the systems behavior that includes notions of robustness, heterogeneity, and/or regimeshift detection. Recently, to explore such functional properties, a convenient representation has been to model such dynamical systems as a weighted graph consisting of a finite, but very large number of interacting agents. This said, there exists very limited relevant statistical theory that is able cope with real-life data, i.e., how does perform simple analysis and/or statistics over a "family" of networks as opposed to a specific network or network-to-network variation. Here, we are interested in the analysis of network families whereby each network represents a "point" on an underlying statistical manifold. From this, we explore the Riemannian structure of the statistical (tensor) manifold in order to define notions of "geodesics" or shortest distance amongst such points as well as a statistical framework for time-varying complex networks for which we can utilize in higher order classification tasks.