Dynamic behaviors of a delay differential equation model of plankton allelopathy

AbstractIn this paper, we consider a modified delay differential equation model of the growth of n-species of plankton having competitive and allelopathic effects on each other. We first obtain the sufficient conditions which guarantee the permanence of the system. As a corollary, for periodic case, we obtain a set of delay-dependent condition which ensures the existence of at least one positive periodic solution of the system. After that, by means of a suitable Lyapunov functional, sufficient conditions are derived for the global attractivity of the system. For the two-dimensional case, under some suitable assumptions, we prove that one of the components will be driven to extinction while the other will stabilize at a certain solution of a logistic equation. Examples show the feasibility of the main results

Chaos to Permanence - Through Control Theory

Work by Cushing et al. [18] and Kot et al. [60] demonstrate that chaotic behavior does occur in biological systems. We demonstrate that chaotic behavior can enable the survival/thriving of the species involved in a system. We adopt the concepts of persistence/permanence as measures of survival/thriving of the species [35]. We utilize present chaotic behavior and a control algorithm based on [66, 72] to push a non-permanent system into permanence. The algorithm uses the chaotic orbits present in the system to obtain the desired state. We apply the algorithm to a Lotka-Volterra type two-prey, one-predator model from [30], a ratio-dependent one-prey, two-predator model from [35] and a simple prey-specialist predator-generalist predator (for ex: plant-insect pest-spider) interaction model [67] and demonstrate its effectiveness in taking advantage of chaotic behavior to achieve a desirable state for all species involved

Chaos to Permanence-Through Control Theory

Work by Cushing et al. \cite{Cushing} and Kot et al. \cite{Kot} demonstrate that chaotic behavior does occur in biological systems. We demonstrate that chaotic behavior can enable the survival/thriving of the species involved in a system. We adopt the concepts of persistence/permanence as measures of survival/thriving of the species \cite{EVG}. We utilize present chaotic behavior and a control algorithm based on \cite{Vincent97,Vincent2001} to push a non-permanent system into permanence. The algorithm uses the chaotic orbits present in the system to obtain the desired state. We apply the algorithm to a Lotka-Volterra type two-prey, one-predator model from \cite{Harvesting}, a ratio-dependent one-prey, two-predator model from \cite{EVG} and a simple prey-specialist predator-generalist predator (for ex: plant-insect pest-spider) interaction model \cite{Upad} and demonstrate its effectiveness in taking advantage of chaotic behavior to achieve a desirable state for all species involved

Smart Grid communications in high traffic environments

The establishment of a previously non-existent data class known as the Smart Grid will pose many difficulties on current and future communication infrastructure. It is imperative that the Smart Grid (SG), as the reactionary and monitory arm of the Power Grid (PG), be able to communicate effectively between grid controllers and individual User Equipment (UE). By doing so, the successful implementation of SG applications can occur, including support for higher capacities of Renewable Energy Resources. As the SG matures, the number of UEs required is expected to rise increasing the traffic in an already burdened communications network. This thesis aims to optimally allocate radio resources such that the SG Quality of Service (QoS) requirements are satisfied with minimal effect on pre-existing traffic. To address this resource allocation problem, a Lotka-Volterra (LV) based resource allocation and scheduler was developed due to its ability to easily adapt to the dynamics of a telecommunications environment. Unlike previous resource allocation algorithms, the LV scheme allocated resources to each class as a function of its growth rate. By doing so, the QoS requirements of the SG were satisfied, with minimal effect on pre-existing traffic. Class queue latencies were reduced by intelligent scheduling of periodic traffic and forward allocation of resources. This thesis concludes that the SG will have a large effect on the telecommunications environment if not successfully controlled and monitored. This effect can be minimized by utilizing the proposed LV based resource allocation and scheduler system. Furthermore, it was shown that the allocation of periodic SG radio channels was optimized by continual updates of the LV model. This ensured the QoS requirements of the SG are achieved and provided enhanced performance. Successful integration of SG UEs in a wireless network can pave the way for increased capacity of Renewable and Intermittent Energy Resources operating on the PG