Search results for: invariant manifold

Authors: Zainab Al-Maamari, Yassir Dinar

Abstract:

The orbit space of an irreducible representation of a finite group is a variety with the ring of invariant polynomials as a coordinate ring. The invariant ring is a polynomial ring if and only if the representation is a reflection representation. Boris Dubrovin shows that the orbits spaces of irreducible real reflection representations acquire the structure of polynomial Frobenius manifolds. Dubrovin's method was also used to construct different examples of Frobenius manifolds on certain reflection representations. By successfully applying Dubrovin’s method on non-polynomial invariant rings of linear representations of dicyclic groups, it gives some results that magnify the relation between invariant theory and Frobenius manifolds.

Keywords: invariant ring, Frobenius manifold, inversion, representation theory

Procedia PDF Downloads 64

Authors: Mancho Manev

Abstract:

The concept of almost paracontact Riemannian manifolds (abbr., apcR manifolds) was introduced by I. Sato in 1976 as an analogue of almost contact Riemannian manifolds. The notion of an apcR manifold of type (p,q) was defined by S. Sasaki in 1980, where p and q are respectively the numbers of the multiplicity of the structure eigenvalues 1 and -1. It also has a simple eigenvalue of 0. In our work, we consider (2n+1)-dimensional apcR manifolds of type (n,n), i.e., the paracontact distribution of the studied manifold can be considered as a 2n-dimensional almost paracomplex Riemannian distribution with almost paracomplex structure and structure group O(n) × O(n). The aim of the present study is to introduce a new class of apcR manifolds. Such a manifold is obtained using the construction of a certain Riemannian cone over it, and the resulting manifold is a paraholomorphic paracomplex Riemannian manifold (abbr., phpcR manifold). We call it a para-Sasaki-like Riemannian manifold (abbr., pSlR manifold) and give some explicit examples. We study the structure of pSlR spaces and find that the paracontact form η is closed and each pSlR manifold locally can be considered as a certain product of the real line with a phpcR manifold, which is locally a Riemannian product of two equidimensional Riemannian spaces. We also obtain that the curvature of the pSlR manifolds is completely determined by the curvature of the underlying local phpcR manifold. Moreover, the ξ-directed Ricci curvature is equal to -2n, while in the Sasaki case, it is 2n. Accordingly, the pSlR manifolds can be interpreted as the counterpart of the Sasaki manifolds; the skew-symmetric part of ∇η vanishes, while in the Sasaki case, the symmetric part vanishes. We define a hyperbolic extension of a (complete) phpcR manifold that resembles a certain warped product, and we indicate that it is a (complete) pSlR manifold. In addition, we consider the hyperbolic extension of a phpcR manifold and prove that if the initial manifold is a complete Einstein manifold with negative scalar curvature, then the resulting manifold is a complete Einstein pSlR manifold with negative scalar curvature. In this way, we produce new examples of a complete Einstein Riemannian manifold with negative scalar curvature. Finally, we define and study para contact conformal/homothetic deformations by deriving a subclass that preserves the para-Sasaki-like condition. We then find that if we apply a paracontact homothetic deformation of a pSlR space, we obtain that the Ricci tensor is invariant.

Keywords: almost paracontact Riemannian manifolds, Einstein manifolds, holomorphic product manifold, warped product manifold

Procedia PDF Downloads 183

Authors: Reza Aghayan

Abstract:

Numerically invariant signatures were introduced as a new paradigm of the invariant recognition for visual objects modulo a certain group of transformations. This paper shows that the current formulation suffers from noise and indeterminacy in the resulting joint group-signatures and applies the n-difference technique and the m-mean signature method to minimize their effects. In our experimental results of applying the proposed numerical scheme to generate joint group-invariant signatures, the sensitivity of some parameters such as regularity and mesh resolution used in the algorithm will also be examined. Finally, several interesting observations are made.

Keywords: Euclidean and affine geometry, differential invariant G-signature curves, numerically invariant joint G-signatures, object recognition, noise, indeterminacy

Procedia PDF Downloads 367

Authors: S. Pesina, T. Solonchak

Abstract:

Lexical invariants, being a sort of stereotypes within the frames of ordinary consciousness, are created by the members of a language community as a result of uniform division of reality. The invariant meaning is formed in person’s mind gradually in the course of different actualizations of secondary meanings in various contexts. We understand lexical the invariant as abstract language essence containing a set of semantic components. In one of its configurations it is the basis or all or a number of the meanings making up the semantic structure of the word.

Keywords: lexical invariant, invariant theories, polysemantic word, cognitive linguistics

Procedia PDF Downloads 285

Authors: Barnali Laha

Abstract:

In this paper, we would like to establish some of the properties of slant and hemislant submanifolds of an indefinite trans-Sasakian manifold. We have four sections in this paper. The first section is introductory. In Section 2, we recall some necessary details of an indefinite trans-Sasakian manifold. In Section 3, we have obtained some interesting properties on a totally umbilical slant submanifolds of an indefinite trans-Sasakian manifold. Finally, in Section 4, some results on integrability conditions of the distributions of hemislant submanifolds of an indefinite trans-Sasakian manifold have been obtained.

Keywords: slant submanifold, indefinite trans-Sasakian manifold, hemislant submanifold, integrability conditions

Procedia PDF Downloads 460

Authors: Santu Dey, Arindam Bhattacharyya

Abstract:

The object of the present paper is to study a quarter-symmetric metric connection in a Lorentzian α-Sasakian manifold. We study some curvature properties of Lorentzian α-Sasakian manifold with respect to quarter-symmetric metric connection. We investigate quasi-projectively at, Φ-symmetric, Φ-projectively at Lorentzian α-Sasakian manifolds with respect to quarter-symmetric metric connection. We also discuss Lorentzian α-Sasakian manifold admitting quartersymmetric metric connection satisfying P.S = 0, where P denote the projective curvature tensor with respect to quarter-symmetric metric connection.

Keywords: quarter-symmetric metric connection, Lorentzian alpha-Sasakian manifold, quasi-projectively flat Lorentzian alpha-Sasakian manifold, phi-symmetric manifold

Procedia PDF Downloads 209

Authors: Reza Aghayan

Abstract:

This paper illustrates that numerically invariant joint signatures suffer biases in the resulting signatures. Next, we classify the arising biases as Bias Type 1 and Bias Type 2 and show how they can be removed.

Keywords: Euclidean and affine geometries, differential invariant signature curves, numerically invariant joint signatures, numerical analysis, numerical bias, curve analysis

Procedia PDF Downloads 562

Authors: Ophir Nave

Abstract:

In our research, we present the concept of singularly perturbed vector field (SPVF) method, and its application to thermal explosion of diesel spray combustion. Given a system of governing equations, which consist of hidden Multi-scale variables, the SPVF method transfer and decompose such system to fast and slow singularly perturbed subsystems (SPS). The SPVF method enables us to understand the complex system, and simplify the calculations. Later powerful analytical, numerical and asymptotic methods (e.g method of integral (invariant) manifold (MIM), the homotopy analysis method (HAM) etc.) can be applied to each subsystem. We compare the results obtained by the methods of integral invariant manifold and SPVF apply to spray droplets combustion model. The research deals with the development of an innovative method for extracting fast and slow variables in physical mathematical models. The method that we developed called singular perturbed vector field. This method based on a numerical algorithm applied to global quasi linearization applied to given physical model. The SPVF method applied successfully to combustion processes. Our results were compared to experimentally results. The SPVF is a general numerical and asymptotical method that reveals the hierarchy (multi-scale system) of a given system.

Keywords: polydisperse spray, model reduction, asymptotic analysis, multi-scale systems

Procedia PDF Downloads 192

Authors: Meimei Wen, Chang Nyung Kim

Abstract:

In the current study, three-dimensional liquid metal (LM) magneto-hydrodynamic (MHD) flows in a manifold with three sub-channels under a uniform magnetic field are numerically investigated. In the manifold, the electrical current can cross channel walls, thus having influence on the flow distribution in each sub-channel. A case with various arrangements of electric conductivity for different parts of channel walls is considered, yielding different current distributions as well as flow distributions in each sub-channel. Here, the imbalance of mass flow rates in the three sub-channels is addressed. Meanwhile, predicted are detailed behaviors of the flow velocity, pressure, current and electric potential of LM MHD flows with three sub-channels. Commercial software CFX is used for the numerical simulation of LM MHD flows.

Keywords: CFX, liquid metal, manifold, MHD flow

Procedia PDF Downloads 322

Authors: K. I. M. Guerra, L. A. P. Silva, J. C. Leal

Abstract:

This study aims to understand with more amplitude and clarity the behavior of a porous medium where a pressure wave travels, translated into relative displacements inside the material, using mathematical tools derived from topology and symplectic geometry. The paper starts with a given partial differential equation based on the continuity and conservation theorems to describe the traveling wave through the porous body. A solution for this equation is proposed after all boundary, and initial conditions are fixed, and it’s accepted that the solution lies in a manifold U of purely spatial dimensions and that is embedded in the Real n-dimensional manifold, with spatial and kinetic dimensions. It’s shown that the U manifold of lower dimensions than IRna, where it is embedded, inherits properties of the vector spaces existing inside the topology it lies on. Then, a second manifold (U*), embedded in another space called IRnb of stress dimensions, is proposed and there’s a non-degenerative function that maps it into the U manifold. This relation is proved as a transformation in between two corresponding admissible solutions of the differential equation in distinct dimensions and properties, leading to a more visual and intuitive understanding of the whole dynamic process of a stress wave through a porous medium and also highlighting the dimensional invariance of Terzaghi’s theory for any coordinate system.

Keywords: poremechanics, soil dynamics, symplectic geometry, wave propagation

Procedia PDF Downloads 264

Authors: Hanjong Kim, Changwan Han, Seonghun Park

Abstract:

Heat exchanger manifolds in aircraft play an important role in evenly distributing the fluid entering through the inlet to the heat transfer unit. In order to achieve this requirement, the manifold should be designed to have a light weight by withstanding high internal pressure. Therefore, this study aims at minimizing the weight of the heat exchanger manifold through topology optimization. For topology optimization, the initial design space was created with the inner surface extracted from the currently used manifold model and with the outer surface having a dimension of 243.42 mm of X 74.09 mm X 65 mm. This design space solid model was transformed into a finite element model with a maximum tetrahedron mesh size of 2 mm using ANSYS Workbench. Then, topology optimization was performed under the boundary conditions of an internal pressure of 5.5 MPa and the fixed support for rectangular inlet boundaries by SIMULIA TOSCA. This topology optimization produced the minimized finial volume of the manifold (i.e., 7.3% of the initial volume) based on the given constraints (i.e., 6% of the initial volume) and the objective function (i.e., maximizing manifold stiffness). Weight of the optimized model was 6.7% lighter than the currently used manifold, but after smoothing the topology optimized model, this difference would be bigger. The current optimized model has uneven thickness and skeleton-shaped outer surface to reduce stress concentration. We are currently simplifying the optimized model shape with spline interpolations by reflecting the design characteristics in thickness and skeletal structures from the optimized model. This simplified model will be validated again by calculating both stress distributions and weight reduction and then the validated model will be manufactured using 3D printing processes.

Keywords: topology optimization, manifold, heat exchanger, 3D printing

Procedia PDF Downloads 216

Authors: M. Berrehail, F. Benamira

Abstract:

We study the quantum motion of a particle in the presence of a time- dependent linear potential using an operator invariant that is quadratic in p and linear in q within the framework of the Lewis-Riesenfeld invariant, The special invariant operator proposed in this work is demonstrated to be an Hermitian operator which has an Airy wave packet as its Eigenfunction

Keywords: airy wave packet, ivariant, time-dependent linear potential, unitary transformation

Procedia PDF Downloads 465

Authors: Saroj Bijarnia, Preety Singh

Abstract:

We propose a simple and effective biometrics system based on face verification across aging using a new variant of texture feature, Pyramid Binary Pattern. This employs Local Binary Pattern along with its hierarchical information. Dimension reduction of generated texture feature vector is done using Principal Component Analysis. Support Vector Machine is used for classification. Our proposed method achieves an accuracy of 92:24% and can be used in an automated age-invariant face verification system.

Keywords: biometrics, age invariant, verification, support vector machine

Procedia PDF Downloads 316

Authors: A. Suparmi, C. Cari, M. Yunianto, B. N. Pratiwi

Abstract:

D-dimensional Dirac equations of q-deformed shape invariant potentials were solved using supersymmetric quantum mechanics (SUSY QM) in the case of exact spin symmetry. The D dimensional radial Dirac equation for shape invariant potential reduces to one-dimensional Schrodinger type equation by an appropriate variable and parameter change. The relativistic energy spectra were analyzed by using SUSY QM and shape invariant properties from radial D dimensional Dirac equation that have reduced to one dimensional Schrodinger type equation. The SUSY operator was used to generate the D dimensional relativistic radial wave functions, the relativistic energy equation reduced to the non-relativistic energy in the non-relativistic limit.

Keywords: D-dimensional dirac equation, non-central potential, SUSY QM, radial wave function

Procedia PDF Downloads 319

Authors: Siti Noor Farwina Anwar, Hailiza Kamarulhaili

Abstract:

In this paper, we present the idea of implementing the Integer Sub-Decomposition (ISD) method on elliptic curves with j-invariant 1728. The ISD method was proposed in 2013 to compute scalar multiplication in elliptic curves, which remains to be the most expensive operation in Elliptic Curve Cryptography (ECC). However, the original ISD method only works on integer number field and solve integer scalar multiplication. By extending the method into the complex quadratic field, we are able to solve complex multiplication and implement the ISD method on elliptic curves with j-invariant 1728. The curve with j-invariant 1728 has a unique discriminant of the imaginary quadratic field. This unique discriminant of quadratic field yields a unique efficiently computable endomorphism, which later able to speed up the computations on this curve. However, the ISD method needs three endomorphisms to be accomplished. Hence, we choose all three endomorphisms to be from the same imaginary quadratic field as the curve itself, where the first endomorphism is the unique endomorphism yield from the discriminant of the imaginary quadratic field.

Keywords: efficiently computable endomorphism, elliptic scalar multiplication, j-invariant 1728, quadratic field

Procedia PDF Downloads 168

Authors: Jay Prakash Singh

Abstract:

The aim of the present paper is to study properties of Quasi conformally flat LP-Sasakian manifolds with a coefficient α. In this paper, we prove that a Quasi conformally flat LP-Sasakian manifold M (n > 3) with a constant coefficient α is an η−Einstein and in a quasi conformally flat LP-Sasakian manifold M (n > 3) with a constant coefficient α if the scalar curvature tensor is constant then M is of constant curvature.

Keywords: LP-Sasakian manifolds, quasi-conformal curvature tensor, concircular vector field, torse forming vector field, Einstein manifold

Procedia PDF Downloads 765

Authors: Wei Feilong

Abstract:

In this study, an local invariant generalized Houghtransform (LI-GHT) method is proposed for integrated circuit (IC) visual positioning. The original generalized Hough transform (GHT) is robust to external noise; however, it is not suitable for visual positioning of IC chips due to the four-dimensionality (4D) of parameter space which leads to the substantial storage requirement and high computational complexity. The proposed LI-GHT method can reduce the dimensionality of parameter space to 2D thanks to the rotational invariance of local invariant geometric feature and it can estimate the accuracy position and rotation angle of IC chips in real-time under noise and blur influence. The experiment results show that the proposed LI-GHT can estimate position and rotation angle of IC chips with high accuracy and fast speed. The proposed LI-GHT algorithm was implemented in IC visual positioning system of radio frequency identification (RFID) packaging equipment.

Keywords: Integrated Circuit Visual Positioning, Generalized Hough Transform, Local invariant Generalized Hough Transform, ICpacking equipment

Procedia PDF Downloads 243

Authors: Teoman Ozer, Ozlem Orhan

Abstract:

This study deals with symmetry group properties and conservation laws of partial differential equations. We give a geometrical interpretation of notion of μ-prolongations of vector fields and of the related concept of μ-symmetry for partial differential equations. We show that these are in providing symmetry reduction of partial differential equations and systems and invariant solutions.

Keywords: λ-symmetry, μ-symmetry, classification, invariant solution

Procedia PDF Downloads 280

Authors: Sahil Kapahi

Abstract:

A Formula SAE competition is characterized by typical track layouts having slaloms, tight corners and short straights, which favor a particular range of engine speed for a given set of gear ratios. Therefore, it is imperative that the power-train is optimized for the corresponding engine rpm band. This paper describes the process of designing, simulating and validating an air intake manifold for an inline four cylinder four-stroke internal combustion gasoline engine based on analysis of required vehicle performance. The requirements for the design of subject intake were set considering the rules of FSAE competitions and analysis of engine performance patterns for typical competition scenarios, carried out using OPTIMUMLAP software. Manifold geometry was optimized using results of air flow simulations performed on ANSYS CFX, and subsequent effect of this geometry on the engine was modeled using 1D simulation on Ricardo WAVE. A design was developed to meet the targeted performance standards in terms of engine torque output and volumetric efficiency. Finally, the intake manifold was manufactured and assembled onto the vehicle, and the engine output of the vehicle with the designed intake was studied using a dynamometer. The results of the dynamometer testing were then validated against predicted values derived from the Ricardo WAVE modeling and benefits to performance of the vehicle were established.

Keywords: 1 D Simulation, air flow simulation, ANSYS CFX, four-stroke engine, OPTIMUM LAP, Ricardo WAVE

Procedia PDF Downloads 217

Authors: Maba Boniface Matadi

Abstract:

This paper analyses the model of Malaria endemic from the point of view of the group theoretic approach. The study identified new independent variables that lead to the transformation of the nonlinear model. Furthermore, corresponding determining equations were constructed, and new symmetries were found. As a result, the findings of the study demonstrate of the integrability of the model to present an invariant solution for the Malaria model.

Keywords: group theory, lie symmetry, invariant solutions, malaria

Procedia PDF Downloads 78

Authors: Matthaios Katsanikas

Abstract:

We study the structure of the invariant manifolds of complex unstable periodic orbits of a family of periodic orbits, in a 3D autonomous Hamiltonian system of galactic type, after a transition of this family from stability to complex instability (Hamiltonian Hopf bifurcation). We consider the case of a supercritical Hamiltonian Hopf bifurcation. The invariant manifolds of complex unstable periodic orbits have two kinds of structures. The first kind is represented by a disk confined structure on the 4D space of section. The second kind is represented by a complicated central tube structure that is associated with an extended network of tube structures, strips and flat structures of sheet type on the 4D space of section.

Keywords: dynamical systems, galactic dynamics, chaos, phase space

Procedia PDF Downloads 113

Authors: Michele Aleandri, Matteo Colangeli, Davide Gabrielli

Abstract:

We study a generalization to a continuous setting of the classical Markov chain tree theorem. In particular, we consider an irreducible diffusion process on a metric graph. The unique invariant measure has an atomic component on the vertices and an absolutely continuous part on the edges. We show that the corresponding density at x can be represented by a normalized superposition of the weights associated to metric arborescences oriented toward the point x. A metric arborescence is a metric tree oriented towards its root. The weight of each oriented metric arborescence is obtained by the product of the exponential of integrals of the form ∫a/b², where b is the drift and σ² is the diffusion coefficient, along the oriented edges, for a weight for each node determined by the local orientation of the arborescence around the node and for the inverse of the diffusion coefficient at x. The metric arborescences are obtained by cutting the original metric graph along some edges.

Keywords: diffusion processes, metric graphs, invariant measure, reversibility

Procedia PDF Downloads 134

Authors: Kankeyanathan Kannan

Abstract:

On approximation properties of group C* algebras is everywhere; it is powerful, important, backbone of countless breakthroughs. For a discrete group G, let A(G) denote its Fourier algebra, and let M₀A(G) denote the space of completely bounded Fourier multipliers on G. An approximate identity on G is a sequence (Φn) of finitely supported functions such that (Φn) uniformly converge to constant function 1 In this paper we prove that approximation property pass to free product.

Keywords: approximation property, weakly amenable, strong invariant approximation property, invariant approximation property

Procedia PDF Downloads 648

Authors: Meng Su

Abstract:

High-dimensional data analysis often presents challenges in capturing the complex, nonlinear relationships and manifold structures inherent to the data. This article presents a novel approach that leverages the strengths of two powerful techniques, Diffusion Maps and Diffusion Probabilistic Models (DPMs), to address these challenges. By integrating the dimensionality reduction capability of Diffusion Maps with the data modeling ability of DPMs, the proposed method aims to provide a comprehensive solution for analyzing and generating high-dimensional data. The Diffusion Map technique preserves the nonlinear relationships and manifold structure of the data by mapping it to a lower-dimensional space using the eigenvectors of the graph Laplacian matrix. Meanwhile, DPMs capture the dependencies within the data, enabling effective modeling and generation of new data points in the low-dimensional space. The generated data points can then be mapped back to the original high-dimensional space, ensuring consistency with the underlying manifold structure. Through a detailed example implementation, the article demonstrates the potential of the proposed hybrid approach to achieve more accurate and effective modeling and generation of complex, high-dimensional data. Furthermore, it discusses possible applications in various domains, such as image synthesis, time-series forecasting, and anomaly detection, and outlines future research directions for enhancing the scalability, performance, and integration with other machine learning techniques. By combining the strengths of Diffusion Maps and DPMs, this work paves the way for more advanced and robust data analysis methods.

Keywords: diffusion maps, diffusion probabilistic models (DPMs), manifold learning, high-dimensional data analysis

Procedia PDF Downloads 68

Authors: Lan Du, Yan Wang, Hui Dai

Abstract:

Synthetic aperture radar (SAR) image change detection has recently become a challenging problem owing to the existence of speckle noises. In this paper, an unsupervised distribution-free change detection for SAR image based on scale-invariant feature transform (SIFT) keypoints and segmentation is proposed. Firstly, the noise-robust SIFT keypoints which reveal the blob-like structures in an image are extracted in the log-ratio image to reduce the detection range. Then, different from the traditional change detection which directly obtains the change-detection map from the difference image, segmentation is made around the extracted keypoints in the two original multitemporal SAR images to obtain accurate changed region. At last, the change-detection map is generated by comparing the two segmentations. Experimental results on the real SAR image dataset demonstrate the effectiveness of the proposed method.

Keywords: change detection, Synthetic Aperture Radar (SAR), Scale-Invariant Feature Transformation (SIFT), segmentation

Procedia PDF Downloads 354

Authors: Dongxu Chen, Yipeng Li

Abstract:

This paper presents an information geometry NonlocalMeans(NLM) algorithm for Poisson denoising. NLM estimates a noise-free pixel as a weighted average of image pixels, where each pixel is weighted according to the similarity between image patches in Euclidean space. In this work, every pixel is a Poisson distribution locally estimated by Maximum Likelihood (ML), all distributions consist of a statistical manifold. A NLM denoising algorithm is conducted on the statistical manifold where Fisher information matrix can be used for computing distribution geodesics referenced as the similarity between patches. This approach was demonstrated to be competitive with related state-of-the-art methods.

Keywords: image denoising, Poisson noise, information geometry, nonlocal-means

Procedia PDF Downloads 262

Authors: J. Branstett, V. Gagneux, A. Leleu, B. Levadoux, J. Pascale

Abstract:

This paper presents the interface CONDUCTHOME which controls home automation systems with a Leap Motion using ‘invariant gesture protocols’. The function of this interface is to simplify the interaction of the user with its environment. A hardware part allows the Leap Motion to be carried around the house. A software part interacts with the home automation box and displays the useful information for the user. An objective of this work is the development a natural/invariant/simple gesture control interface to help elder people/people with disabilities.

Keywords: automation, ergonomics, gesture recognition, interoperability

Procedia PDF Downloads 394

Authors: Mehdi Jafari Matehkolaee

Abstract:

In this paper, we have obtained the adjoint of an arbitrary operator (linear and nonlinear) in Hilbert space by introducing an n-dimensional Riemannian manifold. This general formalism covers every linear operator (non – differential) in Hilbert space. In fact, our approach shows that instead of using the adjoint definition of an operator directly, it can be obtained directly by relying on a suitable generalized space according to the action of the operator in question. For the case of nonlinear operators, we have to change the definition of the linear operator adjoint. But here, we have obtained an adjoint of these operators with respect to the definition of the derivative of the operator. As a matter of fact, we have shown one of the straight applications of the ''Frechet derivative'' in the algebra of the operators.

Keywords: adjoint operator, non-linear operator, differentiable operator, manifold

Procedia PDF Downloads 91

Authors: Kushakov Kholmurodjon, Muhammadjonov Akbarshox

Abstract:

This present paper is devoted to a system of second-order nonlinear differential equations with a special right-hand side, exactly, the linear part and a third-order polynomial of a special form. It is shown that for some relations between the parameters, there is a second-order curve in which trajectories leaving the points of this curve remain in the same place. Thus, the curve is invariant with respect to the given system. Moreover, this system is invariant under a non-degenerate linear transformation of variables. The form of this curve, depending on the relations between the parameters and the eigenvalues of the matrix, is proved. All solutions of this system of differential equations are shown analytically.

Keywords: dynamic system, ellipse, hyperbola, Hess system, polar coordinate system

Procedia PDF Downloads 162

Authors: Rahele Mosleh

Abstract:

This paper gives a survey of results on global stability of extended Ross model for malaria by constructing some elegant Lyapunov functions for two cases of epidemic, including disease-free and endemic occasions. The model is a nonlinear seven-dimensional system of ordinary differential equations that simulates this phenomenon in a more realistic fashion. We discuss the existence of positive disease-free and endemic equilibrium points of the model. It is stated that extended Ross model possesses invariant solutions for human and mosquito in a specific domain of the system.

Keywords: global stability, invariant solutions, Lyapunov function, stationary points

Procedia PDF Downloads 139