Dynamical Systems Commons^™

Local Lagged Adapted Generalized Method Of Moments And Applications, Olusegun Michael Otunuga, Gangaram S. Ladde, Nathan G. Ladde

Olusegun Michael Otunuga

In this work, an attempt is made for developing the local lagged adapted generalized method of moments (LLGMM). This proposed method is composed of: (1) development of the stochastic model for continuous-time dynamic process, (2) development of the discrete-time interconnected dynamic model for statistic process, (3) utilization of Euler-type discretized scheme for nonlinear and non-stationary system of stochastic differential equations, (4) development of generalized method of moment/observation equations by employing lagged adaptive expectation process, (5) introduction of the conceptual and computational parameter estimation problem, (6) formulation of the conceptual and computational state estimation scheme and (7) definition of the conditional …

Stochastic Modeling Of Energy Commodity Spot Price Processes With Delay In Volatility, Olusegun Michael Otunuga, Gangaram S. Ladde

Olusegun Michael Otunuga

Employing basic economic principles, we systematically develop both deterministic and stochastic dynamic models for the log-spot price process of energy commodity. Furthermore, treating a diffusion coefficient parameter in the non-seasonal log-spot price dynamic system as a stochastic volatility functional of log-spot price, an interconnected system of stochastic model for log-spot price, expected log-spot price and hereditary volatility process is developed. By outlining the risk-neutral dynamics and pricing, sufficient conditions are given to guarantee that the risk-neutral dynamic model is equivalent to the developed model. Furthermore, it is shown that the expectation of the square of volatility under the risk-neutral measure …

Time Varying Parameter Estimation Scheme For A Linear Stochastic Differential Equation, Olusegun Michael Otunuga

Olusegun Michael Otunuga

In this work, an attempt is made to estimate time varying parameters in a linear stochastic differential equation. By defining mk as the local admissible sample/data observation size at time tk, parameters and state at time tk are estimated using past data on interval [tk−mk+1, tk]. We show that the parameter estimates at each time tk converge in probability to the true value of the parameters being estimated. A numerical simulation is presented by applying the local lagged adapted generalized method of moments (LLGMM) method to the stochastic differential models governing prices of energy …

Finding Positive Solutions Of Boundary Value Dynamic Equations On Time Scale, Olusegun Michael Otunuga

Olusegun Michael Otunuga

This thesis is on the study of dynamic equations on time scale. Most often, the derivatives and anti-derivatives of functions are taken on the domain of real numbers, which cannot be used to solve some models like insect populations that are continuous while in season and then follow a difference scheme with variable step-size. They die out in winter, while the eggs are incubating or dormant; and then they hatch in a new season, giving rise to a non overlapping population. The general idea of my thesis is to find the conditions for having a positive solution of any boundary …

Global Stability Of Nonlinear Stochastic Sei Epidemic Model With Fluctuations In Transmission Rate Of Disease, Olusegun Michael Otunuga

Olusegun Michael Otunuga

We derive and analyze the dynamic of a stochastic SEI epidemic model for disease spread. Fluctuations in the transmission rate of the disease bring about stochasticity in model. We discuss the asymptotic stability of the infection-free equilibrium by first deriving the closed form deterministic (R₀) and stochastic (R₀) basic reproductive number. Contrary to some author’s remark that different diffusion rates have no effect on the stability of the disease-free equilibrium, we showed that even if no epidemic invasion occurs with respect to the deterministic version of the SEI model (i.e., R₀ < 1), epidemic can still grow initially (if R₀ > 1) …

Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

A Companion To The Introduction To Modern Dynamics, David D. Nolte

David D Nolte

Computing The Optimal Path In Stochastic Dynamical Systems, Martha Bauver, Eric Forgoston, Lora Billings

Lora Billings

Computing The Optimal Path In Stochastic Dynamical Systems, Martha Bauver, Eric Forgoston, Lora Billings

Eric Forgoston

Geometric Limits Of Julia Sets Of Maps Z^N + Exp(2Πiθ) As N → ∞, Scott Kaschner, Reaper Romero, David Simmons

Scott Kaschner

We show that the geometric limit as n → ∞ of the Julia sets J(Pn,c) for the maps Pn,c(z) = zn + c does not exist for almost every c on the unit circle. Furthermore, we show that there is always a subsequence along which the limit does exist and equals the unit circle.

Rational Map Of Cp^2 With No Invariant Foliation, Scott Kaschner, Rodrigo Perez, Roland Roeder

Scott Kaschner

Conference Poster presented at: Midwest Dynamical Systems Conference, Champaign/Urbana, IL November 1-3, 2013.

Zespół Energii Odnawialnej I Zrównoważonego Rozwoju (Eozr), Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Fundamental Domain Of Invariant Sets And Applications, Pengfei Zhang

Pengfei Zhang

No abstract provided.

Electrical Current In Sinai Billiards Under General Small Forces, Pengfei Zhang

Pengfei Zhang

No abstract provided.

Determination Of Kinetic Parameters From The Thermogravimetric Data Set Of Biomass Samples, Karol Postawa, Wojciech M. Budzianowski

Wojciech Budzianowski

This article describes methods of the determination of kinetic parameters from the thermogravimetric data set of biomass samples. It presents the methodology of the research, description of the needed equipment, and the method of analysis of thermogravimetric data. It describes both methodology of obtaining quantitative data such as kinetic parameters as well as of obtaining qualitative data like the composition of biomass. The study is focused mainly on plant biomass because it is easy in harvesting and preparation. Methodology is shown on the sample containing corn stover which is subsequently pyrolysed. The investigated sample show the kinetic of first order …

When A Mechanical Model Goes Nonlinear, Lisa D. Humphreys, P. J. Mckenna

Lisa D Humphreys

This paper had its origin in a curious discovery by the first author in research performed with an undergraduate student. The following odd fact was noticed: when a mechanical model of a suspension bridge (linear near equilibrium but allowed to slacken at large distance in one direction) is shaken with a low-frequency periodic force, several different periodic responses can result, many with high-frequency components.

Dimension Of Stablesets And Scrambled Sets In Positive Finite Entropy Systems, Pengfei Zhang

Pengfei Zhang

No abstract provided.

Partially Hyperbolic Sets With Positive Measure And Acip For Partially Hyperbolic Systems, Pengfei Zhang

Pengfei Zhang

No abstract provided.

Pointwise Dimension, Entropy And Lyapunov Exponents For C1 Maps, Pengfei Zhang

Pengfei Zhang

No abstract provided.

Diffeomorphisms With Global Dominated Splittings Can Not Be Minimal, Pengfei Zhang

Pengfei Zhang

No abstract provided.

Nonlinear Waves And Solitons On Contours And Closed Surfaces, Andrei Ludu

Andrei Ludu

No abstract provided.

Hydrogen Production From Biogas By Oxy-Reforming: Reaction System Analysis, Aleksandra Terlecka, Wojciech M. Budzianowski

Wojciech Budzianowski

Oxy-reforming is emerging as an interesting alternative to conventional methods of hydrogen generation. The current article characterises this process through analysis of individual reactions: SMR (steam methane reforming), WGS (water gas shift) and CPO (catalytic partial oxidation). Analyses relate to optimisation of thermal conditions thus enabling cost-effectivenes of the process.

Exponential Growth Rate Of Paths And Its Connection With Dynamics, Pengfei Zhang

Pengfei Zhang

No abstract provided.

Analysis And Classification Of Nonlinear Dispersive Evolution Equations In The Potential Representation, Andrei Ludu

Andrei Ludu

No abstract provided.

Sliding Mode Control Of The Systems With Uncertain Direction Of Control Vector, Sergey V. Drakunov

Sergey V. Drakunov

No abstract provided.

Sliding-Mode Observers Based On Equivalent Control Method, Sergey V. Drakunov

Sergey V. Drakunov

No abstract provided.