• Honam Mathematical Journal
• /
• v.44 no.3
• /
• pp.402-418
• /
• 2022

Noise is a fundamental factor to increased validity and regularity of spike propagation and neuronal firing in the nervous system. In this paper, we examine the stochastic version of the Izhikevich-FitzHugh neuron dynamical model. This approach is based on techniques presented by Luo and Guo, which provide a general framework for the bifurcation and stability analysis of two dimensional stochastic dynamical system as an Itô averaging diffusion system. By using largest lyapunov exponent, local and global stability of the stochastic system at the equilibrium point are investigated. We focus on the two kinds of stochastic bifurcations: the P-bifurcation and the D-bifurcations. By use of polar coordinate, Taylor expansion and stochastic averaging method, it is shown that there exists choices of diffusion and drift parameters such that these bifurcations occurs. Finally, numerical simulations in various viewpoints, including phase portrait, evolution in time and probability density, are presented to show the effects of the diffusion and drift coefficients that illustrate our theoretical results.

• Honam Mathematical Journal
• /
• v.39 no.3
• /
• pp.401-416
• /
• 2017

Fractional kinetic equations are investigated in order to describe the various phenomena governed by anomalous reaction in dynamical systems with chaotic motion. Many authors have provided solutions of various families of fractional kinetic equations involving special functions. Here, in this paper, we aim at presenting solutions of certain general families of fractional kinetic equations using Prabhakar-type operators. The idea of present paper is motivated by Tomovski et al. [21].

• 제어로봇시스템학회:학술대회논문집
• /
• 1990.10a
• /
• pp.439-445
• /
• 1990

All models of dynamical systems invariably have some measure of uncertainties associated with some of their dynamics. The recent approaches to establish robustness of stabilizing feedback control against the possible uncertainties have a serious limitation, that is their applicability only to the systems that satisfy the matching conditions. Such conditions are rarely met in general applications. If a particular system satisfies the matching conditions, the addition of an actuator will destroy the satisfaction of such conditions. In this paper, we develop robust control algorithm for uncertain multivariable systems in which the matching conditions are not necessarily met. We empoly Lyapunov's second method to derive robust stabilizing controllers which guarantee asymptotic stability against prescribed uncertainties. The derivation consists of transforming the original uncertain system to controllable canonical form and constructing a constant switching surface by designing the closed-loop characteristics as a function of the uncertainties. Numerical examples are discussed as illustrations.

• 제어로봇시스템학회:학술대회논문집
• /
• 1998.10a
• /
• pp.451-454
• /
• 1998

This paper proposes a new method of Model Predictive Control (MPC) of nonlinear process by us-ing the measured Volterra kernels as the nonlinear model. A nonlinear dynamical process is usually de-scribed as Volterra kernel representation, In the authors' method, a pseudo-random M-sequence is ar plied to the nonlinear process, and its output is measured. Taking the crosscorrelation between the input and output, we obtain the Volterra kernels up to 3rd order which represent the nonlinear characteristics of the process. By using the measured Volterra kernels, we can construct the nonlinear model for MPC. In applying Model Predictive Control to a nonlinear process, the most important thing is, in general, what kind of nonlinear model should be used. The authors used the measured Volterra kernels of up to 3rd order as the process model. The authors have carried out computer simulations and compared the simulation results for the linear model, the nonlinear model up to 2nd Volterra kernel, and the nonlinear model up to 3rd order Vol-terra kernel. The results of computer simulation show that the use of Valterra kernels of up to 3rd order is most effective for Model Predictive Control of nonlinear dynamical processes.

• Proceedings of the KOSOMBE Conference
• /
• v.1992 no.05
• /
• pp.129-132
• /
• 1992

Cellular kinetics formulate the basis of tumor immune system dynamics which may be synthesized mathematically as cascades of bilinear systems which are connected by nonlinear dynamical terms. In this manner, a foundation for the control of syngeneic tumors is presented. We have analyzed the mechanisms of controlling the infiltration of lymphocytes into tumor tissues. Simulated anneal ins, a general-purpose method of multivariate optimization, is applied to combinatorial optimization, which is to find the minimum of a given function depending on many parameters. We compare the results of the different methods including the global optimization algorithm, known as simutated annealing.

• Journal of The Korean Astronomical Society
• /
• v.40 no.4
• /
• pp.91-97
• /
• 2007

The Fokker-Planck (FP) model is one of the commonly used methods for studies of the dynamical evolution of dense spherical stellar systems such as globular clusters and galactic nuclei. The FP model is numerically stable in most cases, but we find that it encounters numerical difficulties rather often when the effects of tidal shocks are included in two-dimensional (energy and angular momentum space) version of the FP model or when the initial condition is extreme (e.g., a very large cluster mass and a small cluster radius). To avoid such a problem, we have developed a new integration scheme for a two-dimensional FP equation by adopting an Alternating Direction Implicit (ADI) method given in the Douglas-Rachford split form. We find that our ADI method reduces the computing time by a factor of ${\sim}2$ compared to the fully implicit method, and resolves problems of numerical instability.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 1998.10a
• /
• pp.354-360
• /
• 1998

In general, it is very difficult to find optimal fuzzy rules by experience when a system is dynamical and/or complex. Futhermore proper fuzzy partitioning is not deterministic and there is no unique solution. Therefore we propose a new design method of an optimal fuzzy logic controller, that is a co-evolutionary genetic algorithm finding optimal fuzzy rule and proper membership functions at the same time. We formalize the relation between fuzzy rules and membership functions in terms of fitness. We review the typical approaching methods to co-evolutionary genetic algorithms , and then classify them by fitness relation matrix. Applications of the proposed method to a path planning problem of autonomous mobile robots when moving objects exist are presented to demonstrate the performance and effectiveness of the method.

• Advances in nano research
• /
• v.16 no.2
• /
• pp.175-186
• /
• 2024

Dynamical behaviors of one-dimensional (1D) nano-sized structures are of great importance in nanotechnology applications. Therefore, the torsional dynamic response of functionally graded nanorods which could be used to model the nano electromechanical systems or micro electromechanical systems with torsional motion about the center of twist is examined based on the theory of strain gradient nonlocal elasticity in this work. The mathematical background is constructed based on both strain gradient theory and Eringen's nonlocal elasticity theory. The equation of motions and boundary conditions of radially functionally graded nanorods are derived using Hamilton's principle and then transformed into the eigenvalue analysis by using Fourier sine series. A general coefficient matrix is obtained to assemble the Stokes' transformation. The case of a restrained functionally graded nanorod embedded in two elastic springs against torsional rotation is then deeply investigated. The effect of changing the functionally graded index, the stiffness of elastic boundary conditions, the length scale parameter and nonlocal parameter are investigated in detail.

• Proceedings of the KIEE Conference
• /
• 1991.07a
• /
• pp.670-677
• /
• 1991

All models of dynamical systems invariably have some measure of uncertainties associated with some of their dynamics. The recent approaches to establish robustness of stabilizing feedback control against the possible uncertainties have a serious limitation, that is, their applicability only to the systems that satisfy the matching conditions. Such conditions are rarely met in general applications. If a particular system satisfies the matching conditions, the addition of an actuator will destroy the satisfaction of such conditions. In this paper, we develop robust control algorithm for uncertain multivariable systems in which the matching conditions are not necessarily met. In order to eliminate an influence over partial state variables due to unknown constant disturbances we perform the appropriate block-decomposition for a given system. Functional observers are introduced to estimate the unknown constant disturbances. The sliding mode controller is designed in such a way that the partial state variables in the state-space are directed towards switching surfaces and regulated to the origin asymptotically. Numerical examples are discussed as illustrations.

• Publications of The Korean Astronomical Society
• /
• v.32 no.1
• /
• pp.55-57
• /
• 2017

Presently, the number of known asteroids is more than 710,000. Knowledge of size and albedo is essential in many aspects of asteroid research, such as the chemical composition and mineralogy, the size-frequency distribution of dynamical families, and the relationship between small bodies in the outer solar system or comets. Recently, based on the infrared all-sky survey data obtained by IRAS, AKARI, and WISE, the large asteroid catalogs containing size and albedo data have been constructed. In this paper, we discuss the compositional distribution in the main belt regions based on the compiled data on size, albedo, and separately obtained taxonomic type information.