Search results for: shifting function method

Authors: Saleem Z. Ramadan, Gürsel A. Süer

Abstract:

In this paper a genetic algorithm (GA) with dual-fitness function is proposed and applied to solve the deterministic identical machine scheduling problem. The mating fitness function value was used to determine the mating for chromosomes, while the selection fitness function value was used to determine their survivals. The performance of this algorithm was tested on deterministic identical machine scheduling using simulated data. The results obtained from the proposed GA were compared with classical GA and integer programming (IP). Results showed that dual-fitness function GA outperformed the classical single-fitness function GA with statistical significance for large problems and was competitive to IP, particularly when large size problems were used.

Keywords: Machine scheduling, Genetic algorithms, Due dates, Number of tardy jobs, Number of early jobs, Integer programming, Dual Fitness functions.

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Authors: V. Rashtchi, R. Aghmasheh

Abstract:

Detection of squirrel cage induction motor (SCIM) broken bars has long been an important but difficult job in the detection area of motor faults. Early detection of this abnormality in the motor would help to avoid costly breakdowns. A new detection method based on particle swarm optimization (PSO) is presented in this paper. Stator current in an induction motor will be measured and characteristic frequency components of faylted rotor will be detected by minimizing a fitness function using pso. Supply frequency and side band frequencies and their amplitudes can be estimated by the proposed method. The proposed method is applied to a faulty motor with one and two broken bars in different loading condition. Experimental results prove that the proposed method is effective and applicable.

Keywords: broken bar, PSO, fault detection, SCIM

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Authors: Jesús Everardo Olguín Tiznado, Rafael García Martínez, Claudia Camargo Wilson, Juan Andrés López Barreras, Everardo Inzunza González, Javier Ordorica Villalvazo

Abstract:

The response surface methodology (RSM) is a collection of mathematical and statistical techniques useful in the modeling and analysis of problems in which the dependent variable receives the influence of several independent variables, in order to determine which are the conditions under which should operate these variables to optimize a production process. The RSM estimated a regression model of first order, and sets the search direction using the method of maximum / minimum slope up / down MMS U/D. However, this method selects the step size intuitively, which can affect the efficiency of the RSM. This paper assesses how the step size affects the efficiency of this methodology. The numerical examples are carried out through Monte Carlo experiments, evaluating three response variables: efficiency gain function, the optimum distance and the number of iterations. The results in the simulation experiments showed that in response variables efficiency and gain function at the optimum distance were not affected by the step size, while the number of iterations is found that the efficiency if it is affected by the size of the step and function type of test used.

Keywords: RSM, dependent variable, independent variables, efficiency, simulation

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Authors: Christiono Utomo, Arazi Idrus, Isnanto, Annisa Nugraheni, Farida Rahmawati

Abstract:

A Negotiation Support is required on a value-based decision to enable each stakeholder to evaluate and rank the solution alternatives before engaging into negotiation with the other stakeholders. This study demonstrates a process of negotiation support model for selection of a building system from value-based design perspective. The perspective is based on comparison of function and cost of a building system. Multi criteria decision techniques were applied to determine the relative value of the alternative solutions for performing the function. A satisfying option game theory are applied to the criteria of value-based decision which are LCC (life cycle cost) and function based FAST. The results demonstrate a negotiation process to select priorities of a building system. The support model can be extended to an automated negotiation by combining value based decision method, group decision and negotiation support.

Keywords: NSS, Value-based, Decision, Construction.

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Authors: Amin Aghatabar Roodbary, Mohammad Hassan Bastani

Abstract:

One of the defects of stepped frequency radar systems is their sensitivity to target motion. In such systems, target motion causes range cell shift, false peaks, Signal to Noise Ratio (SNR) reduction and range profile spreading because of power spectrum interference of each range cell in adjacent range cells which induces distortion in High Resolution Range Profile (HRRP) and disrupt target recognition process. Thus Target Motion Parameters (TMPs) effects compensation should be employed. In this paper, such a method for estimating TMPs (velocity and acceleration) and consequently eliminating or suppressing the unwanted effects on HRRP based on entropy minimization has been proposed. This method is carried out in two major steps: in the first step, a discrete search method has been utilized over the whole acceleration-velocity lattice network, in a specific interval seeking to find a less-accurate minimum point of the entropy function. Then in the second step, a 1-D search over velocity is done in locus of the minimum for several constant acceleration lines, in order to enhance the accuracy of the minimum point found in the first step. The provided simulation results demonstrate the effectiveness of the proposed method.

Keywords: ATR, HRRP, motion compensation, SFW, TMP.

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Authors: Junji Kaneko, Shigeyuki Haruyama, Ken Kaminishi, Tadayuki Kyoutani, Siti Ruhana Omar, Oke Oktavianty

Abstract:

This study is used as a definition method to the value and function in manufacturing sector. In concurrence of discussion about present condition of modeling method, until now definition of 1D-CAE is ambiguity and not conceptual. Across all the physic fields, those methods are defined with the formulation of differential algebraic equation which only applied time derivation and simulation. At the same time, we propose semi-acausal modeling concept and differential algebraic equation method as a newly modeling method which the efficiency has been verified through the comparison of numerical analysis result between the semi-acausal modeling calculation and FEM theory calculation.

Keywords: System Model, Physical Models, Empirical Models, Conservation Law, Differential Algebraic Equation, Object-Oriented.

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Authors: Wen-Chi Liu

Abstract:

This study applies the sequential panel selection method (SPSM) procedure proposed by Chortareas and Kapetanios (2009) to investigate the time-series properties of energy consumption in 50 US states from 1963 to 2009. SPSM involves the classification of the entire panel into a group of stationary series and a group of non-stationary series to identify how many and which series in the panel are stationary processes. Empirical results obtained through SPSM with the panel KSS unit root test developed by Ucar and Omay (2009) combined with a Fourier function indicate that energy consumption in all the 50 US states are stationary. The results of this study have important policy implications for the 50 US states.

Keywords: Energy Consumption, Panel Unit Root, Sequential Panel Selection Method, Fourier Function, US states.

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Authors: Minh T. N. Le, Cathleen Teh, Ng Shyh-Chang, Vladimir Korzh, Harvey F. Lodish, Bing Lim

Abstract:

MicroRNAs are an important class of gene expression regulators that are involved in many biological processes including embryogenesis. miR-125b is a conserved microRNA that is enriched in the nervous system. We have previously reported the function of miR-125b in neuronal differentiation of human cell lines. We also discovered the function of miR-125b in regulating p53 in human and zebrafish. Here we further characterize the brain defects in zebrafish embryos injected with morpholinos against miR-125b. Our data confirm the essential role of miR-125b in brain morphogenesis particularly in maintaining the balance between proliferation, cell death and differentiation. We identified lunatic fringe (lfng) as an additional target of miR-125b in human and zebrafish and suggest that lfng may mediate the function of miR-125b in neurogenesis. Together, this report reveals new insights into the function of miR- 125b during neural development of zebrafish.

Keywords: microRNA, miR-125b, neurogenesis, zebrafish.

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Authors: Yuan Zheng

Abstract:

3D model-based vehicle matching provides a new way for vehicle recognition, localization and tracking. Its key is to construct an evaluation function, also called fitness function, to measure the degree of vehicle matching. The existing fitness functions often poorly perform when the clutter and occlusion exist in traffic scenarios. In this paper, we present a practical and efficient fitness function. Unlike the existing evaluation functions, the proposed fitness function is to study the vehicle matching problem from both local and global perspectives, which exploits the pixel gradient information as well as the silhouette information. In view of the discrepancy between 3D vehicle model and real vehicle, a weighting strategy is introduced to differently treat the fitting of the model’s wireframes. Additionally, a normalization operation for the model’s projection is performed to improve the accuracy of the matching. Experimental results on real traffic videos reveal that the proposed fitness function is efficient and robust to the cluttered background and partial occlusion.

Keywords: 3D-2D matching, fitness function, 3D vehicle model, local image gradient, silhouette information.

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Authors: Rana M. Zeina, Laila AL-Ayadhi, Shahid Bashir

Abstract:

Cognitive symptoms and behavioral symptoms may, in fact, overlap and be related to the level of the general cognitive function. We have measured the behavioral aspects of autism and its correlation to the cognitive ability in 30 children with ASD. We used a neuropsychological Battery CANTAB eclipse to evaluate the ASD children's cognitive ability. Individuals with ASD and challenging behaviors showed significant correlation between some cognitive abilities and Motor aspects. Based on these findings, we can conclude that the motor behavioral problems in autism affect specific cognitive abilities in ASDs such as comprehension, learning, reversal, acquisition, attention set shifting, and speed of reaction to one stimulus. Future researches should also focus on the relationship between motor stereotypes and other subtypes of repetitive behaviors, such as verbal stereotypes, ritual routine adherence, and the use of different types of CANTAB tests.

Keywords: Autism, Cognitive ability, Motor Behavior, and Neuropsychological battery.

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Authors: M. Watanabe, T. Yamaguchi, M. Sasajima, Y. Kurosawa, Y. Koike

Abstract:

Headphones and earphones have many extremely small holes or narrow slits; they use sound-absorbing or porous material (i.e., dampers) to suppress vibratory system resonance. The air viscosity in these acoustic paths greatly affects the acoustic properties. Simulation analyses such as the finite element method (FEM) therefore require knowledge of the material properties of sound-absorbing or porous materials, such as the characteristic impedance and propagation constant. The transfer function method using acoustic tubes is a widely known measuring method, but there is no literature on taking measurements up to the audible range. To measure the acoustic properties at high-range frequencies, the acoustic tubes that form the measuring device need to be narrowed, and the distance between the two microphones needs to be reduced. However, when the tubes are narrowed, the characteristic impedance drops below the air impedance. In this study, we considered the effect of air viscosity in an acoustical tube, introduced a theoretical formula for this effect in the form of complex density and complex sonic velocity, and verified the theoretical formula. We also conducted an experiment and observed the effect from air viscosity in the actual measurements.

Keywords: acoustic tube, air viscosity, earphones, FEM, porous material, sound-absorbing material, transfer function method

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Authors: Sung Hoon Jung

Abstract:

In this paper, we propose a selective mutation method for improving the performances of genetic algorithms. In selective mutation, individuals are first ranked and then additionally mutated one bit in a part of their strings which is selected corresponding to their ranks. This selective mutation helps genetic algorithms to fast approach the global optimum and to quickly escape local optima. This results in increasing the performances of genetic algorithms. We measured the effects of selective mutation with four function optimization problems. It was found from extensive experiments that the selective mutation can significantly enhance the performances of genetic algorithms.

Keywords: Genetic algorithm, selective mutation, function optimization

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Authors: Sadi Vural, Hiromi Tomii, Hironori Yamauchi

Abstract:

As the development of digital technology is increasing, Digital cinema is getting more spread. However, content copy and attack against the digital cinema becomes a serious problem. To solve the above security problem, we propose “Additional Watermarking" for digital cinema delivery system. With this proposed “Additional watermarking" method, we protect content copyrights at encoder and user side information at decoder. It realizes the traceability of the watermark embedded at encoder. The watermark is embedded into the random-selected frames using Hash function. Using it, the embedding position is distributed by Hash Function so that third parties do not break off the watermarking algorithm. Finally, our experimental results show that proposed method is much better than the convenient watermarking techniques in terms of robustness, image quality and its simple but unbreakable algorithm.

Keywords: Decoder, Digital content, JPEG2000 Frame, System-On-Chip and additional watermark.

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Authors: Amal Elmzabi, Mostafa Bellafkih, Mohammed Ramdani

Abstract:

The Chiu-s method which generates a Takagi-Sugeno Fuzzy Inference System (FIS) is a method of fuzzy rules extraction. The rules output is a linear function of inputs. In addition, these rules are not explicit for the expert. In this paper, we develop a method which generates Mamdani FIS, where the rules output is fuzzy. The method proceeds in two steps: first, it uses the subtractive clustering principle to estimate both the number of clusters and the initial locations of a cluster centers. Each obtained cluster corresponds to a Mamdani fuzzy rule. Then, it optimizes the fuzzy model parameters by applying a genetic algorithm. This method is illustrated on a traffic network management application. We suggest also a Mamdani fuzzy rules generation method, where the expert wants to classify the output variables in some fuzzy predefined classes.

Keywords: Fuzzy entropy, fuzzy inference systems, genetic algorithms, network management, subtractive clustering.

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Authors: M. Asato, C. Liu, N. Fujima, T. Hoshino, Y. Chen, T. Mohri

Abstract:

We study the temperature dependence of the interaction energies (IEs) of X (=Ru, Rh) impurities in Pd, due to the Fermi-Dirac (FD) distribution and the thermal vibration effect by the Debye-Grüneisen model. The n-body (n=2~4) IEs among X impurities in Pd, being used to calculate the internal energies in the free energies of the Pd-rich PdX alloys, are determined uniquely and successively from the lower-order to higher-order, by the full-potential Korringa-Kohn-Rostoker Green’s function method (FPKKR), combined with the generalized gradient approximation in the density functional theory. We found that the temperature dependence of IEs due to the FD distribution, being usually neglected, is very important to reproduce the X-concentration dependence of the observed solvus temperatures of the Pd-rich PdX (X=Ru, Rh) alloys.

Keywords: Full-potential KKR-Green’s function method, Fermi-Dirac distribution, GGA, phase diagram of Pd-rich PdX (X=Ru, Rh) alloys, thermal vibration effect.

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Authors: Ping He

Abstract:

This paper addresses the problem of the partial state feedback stabilization of a class of nonlinear systems. In order to stabilization this class systems, the especial place of this paper is to reverse designing the state feedback control law from the method of judging system stability with the center manifold theory. First of all, the center manifold theory is applied to discuss the stabilization sufficient condition and design the stabilizing state control laws for a class of nonlinear. Secondly, the problem of partial stabilization for a class of plane nonlinear system is discuss using the lyapunov second method and the center manifold theory. Thirdly, we investigate specially the problem of the stabilization for a class of homogenous plane nonlinear systems, a class of nonlinear with dual-zero eigenvalues and a class of nonlinear with zero-center using the method of lyapunov function with homogenous derivative, specifically. At the end of this paper, some examples and simulation results are given show that the approach of this paper to this class of nonlinear system is effective and convenient.

Keywords: Partial stabilization, Nonlinear critical systems, Centermanifold theory, Lyapunov function, System reduction.

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Authors: Clio G. Vossou, Ioannis N. Koukoulis, Christopher G. Provatidis

Abstract:

The present work encounters the solution of the defect identification problem with the use of an evolutionary algorithm combined with a simplex method. In more details, a Matlab implementation of Genetic Algorithms is combined with a Simplex method in order to lead to the successful identification of the defect. The influence of the location and the orientation of the depressed ellipsoidal flaw was investigated as well as the use of different amount of static data in the cost function. The results were evaluated according to the ability of the simplex method to locate the global optimum in each test case. In this way, a clear impression regarding the performance of the novel combination of the optimization algorithms, and the influence of the geometrical parameters of the flaw in defect identification problems was obtained.

Keywords: Defect identification, genetic algorithms, optimization.

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Authors: Sadi Vural, Hiromi Tomii, Hironori Yamauchi

Abstract:

As far as the latest technological improvements are concerned, digital systems more become popular than the past. Despite this growing demand to the digital systems, content copy and attack against the digital cinema contents becomes a serious problem. To solve the above security problem, we propose “traceable watermarking using Hash functions for digital cinema system. Digital Cinema is a great application for traceable watermarking since it uses watermarking technology during content play as well as content transmission. The watermark is embedded into the randomly selected movie frames using CRC-32 techniques. CRC-32 is a Hash function. Using it, the embedding position is distributed by Hash Function so that any party cannot break off the watermarking or will not be able to change. Finally, our experimental results show that proposed DWT watermarking method using CRC-32 is much better than the convenient watermarking techniques in terms of robustness, image quality and its simple but unbreakable algorithm.

Keywords: Decoder, Digital content, JPEG2000 Frame, System-On-Chip, traceable watermark, Hash Function, CRC-32.

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Authors: Sufian Ashraf Mazhari, Surendra Kumar

Abstract:

In this paper performance of Puma 560 manipulator is being compared for hybrid gradient descent and least square method learning based ANFIS controller with hybrid Genetic Algorithm and Generalized Pattern Search tuned radial basis function based Neuro-Fuzzy controller. ANFIS which is based on Takagi Sugeno type Fuzzy controller needs prior knowledge of rule base while in radial basis function based Neuro-Fuzzy rule base knowledge is not required. Hybrid Genetic Algorithm with generalized Pattern Search is used for tuning weights of radial basis function based Neuro- fuzzy controller. All the controllers are checked for butterfly trajectory tracking and results in the form of Cartesian and joint space errors are being compared. ANFIS based controller is showing better performance compared to Radial Basis Function based Neuro-Fuzzy Controller but rule base independency of RBF based Neuro-Fuzzy gives it an edge over ANFIS

Keywords: Neuro-Fuzzy, Robotic Control, RBFNF, ANFIS, Hybrid GA.

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Authors: Yuzhi Cai

Abstract:

In this talk, we introduce a newly developed quantile function model that can be used for estimating conditional distributions of financial returns and for obtaining multi-step ahead out-of-sample predictive distributions of financial returns. Since we forecast the whole conditional distributions, any predictive quantity of interest about the future financial returns can be obtained simply as a by-product of the method. We also show an application of the model to the daily closing prices of Dow Jones Industrial Average (DJIA) series over the period from 2 January 2004 - 8 October 2010. We obtained the predictive distributions up to 15 days ahead for the DJIA returns, which were further compared with the actually observed returns and those predicted from an AR-GARCH model. The results show that the new model can capture the main features of financial returns and provide a better fitted model together with improved mean forecasts compared with conventional methods. We hope this talk will help audience to see that this new model has the potential to be very useful in practice.

Keywords: DJIA, Financial returns, predictive distribution, quantile function model.

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Authors: Nisha Goyal, R.K. Gupta

Abstract:

This paper presents a new function expansion method for finding traveling wave solutions of a nonlinear equations and calls it the G G -expansion method, given by Wang et al recently. As an application of this new method, we study the well-known Sawada-Kotera-Kadomtsev-Petviashivili equation and Bogoyavlensky-Konoplechenko equation. With two new expansions, general types of soliton solutions and periodic solutions for these two equations are obtained.

Keywords: Sawada-Kotera-Kadomtsev-Petviashivili equation, Bogoyavlensky-Konoplechenko equation,

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Authors: Gamze Ozel, Selen Cakmakyapan

Abstract:

We introduce a new model called the Marshall-Olkin Rayleigh distribution which extends the Rayleigh distribution using Marshall-Olkin transformation and has increasing and decreasing shapes for the hazard rate function. Various structural properties of the new distribution are derived including explicit expressions for the moments, generating and quantile function, some entropy measures, and order statistics are presented. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The potentiality of the new model is illustrated by means of a simulation study. 

Keywords: Marshall-Olkin distribution, Rayleigh distribution, estimation, maximum likelihood.

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Authors: Abdulrahman S. Alturki, John S. Loomis

Abstract:

This paper discusses a corner detection algorithm for camera calibration. Calibration is a necessary step in many computer vision and image processing applications. Robust corner detection for an image of a checkerboard is required to determine intrinsic and extrinsic parameters. In this paper, an algorithm for fully automatic and robust X-corner detection is presented. Checkerboard corner points are automatically found in each image without user interaction or any prior information regarding the number of rows or columns. The approach represents each X-corner with a quadratic fitting function. Using the fact that the X-corners are saddle points, the coefficients in the fitting function are used to identify each corner location. The automation of this process greatly simplifies calibration. Our method is robust against noise and different camera orientations. Experimental analysis shows the accuracy of our method using actual images acquired at different camera locations and orientations.

Keywords: Camera Calibration, Corner Detector, Saddle Points, X-Corners.

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Authors: Ali Dehgan Moroozeh, B. Farhadi Bansouleh

Abstract:

Evapotranspiration is one of the most important components of the hydrological cycle. Evapotranspiration (ETo) is an important variable in water and energy balances on the earth’s surface, and knowledge of the distribution of ET is a key factor in hydrology, climatology, agronomy and ecology studies. Many researchers have a valid relationship, which is a function of climate factors, to estimate the potential evapotranspiration presented to the plant water stress or water loss, prevent. The FAO-Penman method (PM) had been recommended as a standard method. This method requires many data and these data are not available in every area of world. So, other methods should be evaluated for these conditions. When sufficient or reliable data to solve the PM equation are not available then Hargreaves equation can be used. The Hargreaves equation (HG) requires only daily mean, maximum and minimum air temperature extraterrestrial radiation .In this study, Hargreaves method (HG) were evaluated in 12 stations in the North West region of Iran. Results of HG and M.HG methods were compared with results of PM method. Statistical analysis of this comparison showed that calibration process has had significant effect on efficiency of Hargreaves method.

Keywords: Evapotranspiration, Hargreaves equation, FAOPenman method.

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Authors: Takashi Mitsuishi, Koji Saigusa

Abstract:

This paper presents circular polar coordinates transformation of periodic fuzzy membership function. The purpose is identification of domain of periodic membership functions in consequent part of IF-THEN rules. Proposed methods in this paper remove complicatedness concerning domain of periodic membership function from defuzzification in fuzzy approximate reasoning. Defuzzification on circular polar coordinates is also proposed.

Keywords: Defuzzification, periodic membership function, polar coordinates transformation.

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Authors: S. Lecheb, A. Nour, A. Chellil, A. Basta, D. Belmiloud, H. Kebi

Abstract:

In recent years, a new numerical method has been developed, the extended finite element method (X-FEM). The objective of this work is to exploit the (X-FEM) for the treatment of the fracture mechanics problems on 3D geometries, where we showed the ability of this method to simulate the fatigue crack growth into two cases: edge and central crack. In the results we compared the six first natural frequencies of mode shapes uncracking with the cracking initiation in the structure, and showed the stress intensity factor (SIF) evolution function as crack size propagation into structure, the analytical validation of (SIF) is presented. For to evidence the aspects of this method, all result is compared between FEA and X-FEM.

Keywords: 3D fatigue crack growth, FEA, natural frequencies, stress intensity factor (SIF), X-FEM.

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Authors: Anjali Verma, Ram Jiwari, Jitender Kumar

Abstract:

This paper presents a new function expansion method for finding traveling wave solution of a non-linear equation and calls it the (G'/G)-expansion method. The shallow water wave equation is reduced to a non linear ordinary differential equation by using a simple transformation. As a result the traveling wave solutions of shallow water wave equation are expressed in three forms: hyperbolic solutions, trigonometric solutions and rational solutions.

Keywords: Shallow water wave equation, Exact solutions, (G'/G) expansion method.

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Authors: Jay Singh, Kalyan Chatterjee, C. B. Vishwakarma

Abstract:

A mixed method by combining a Eigen algorithm and improved pade approximations is proposed for reducing the order of the large-scale dynamic systems. The most dominant Eigen value of both original and reduced order systems remain same in this method. The proposed method guarantees stability of the reduced model if the original high-order system is stable and is comparable in quality with the other well known existing order reduction methods. The superiority of the proposed method is shown through examples taken from the literature.

Keywords: Eigen algorithm, Order reduction, improved pade approximations, Stability, Transfer function.

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Authors: Jeries J. Abou-Hanna

Abstract:

Several techniques exist for determining stress-intensity factors in linear elastic fracture mechanics analysis. These techniques are based on analytical, numerical, and empirical approaches that have been well documented in literature and engineering handbooks. However, not all techniques share the same merit. In addition to overly-conservative results, the numerical methods that require extensive computational effort, and those requiring copious user parameters hinder practicing engineers from efficiently evaluating stress-intensity factors. This paper investigates the prospects of reducing the complexity and required variables to determine stress-intensity factors through the utilization of the stress gradient and a weighting function. The heart of this work resides in the understanding that fracture emanating from stress concentration locations cannot be explained by a single maximum stress value approach, but requires use of a critical volume in which the crack exists. In order to understand the effectiveness of this technique, this study investigated components of different notch geometry and varying levels of stress gradients. Two forms of weighting functions were employed to determine stress-intensity factors and results were compared to analytical exact methods. The results indicated that the “exponential” weighting function was superior to the “absolute” weighting function. An error band +/- 10% was met for cases ranging from a steep stress gradient in a sharp v-notch to the less severe stress transitions of a large circular notch. The incorporation of the proposed method has shown to be a worthwhile consideration.

Keywords: Fracture mechanics, finite element method, stress intensity factor, stress gradient.

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Authors: R. Kongnuy, E. Naowanich, T. Kruehong

Abstract:

An important technique in stability theory for differential equations is known as the direct method of Lyapunov. In this work we deal global stability properties of Leptospirosis transmission model by age group in Thailand. First we consider the data from Division of Epidemiology Ministry of Public Health, Thailand between 1997-2011. Then we construct the mathematical model for leptospirosis transmission by eight age groups. The Lyapunov functions are used for our model which takes the forms of an Ordinary Differential Equation system. The globally asymptotically for equilibrium states are analyzed.

Keywords: Age Group, Leptospirosis, Lyapunov Function, Ordinary Differential Equation.

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