The influence of time varying inputs on a two layer neural network involving transmission delays and complex valued synaptic connection strengths is studied in this paper. The asymptotic behaviour of solutions of the system is studied for a variety of input functions. Conditions for solutions of a system with time varying inputs to approach the solutions (including equilibrium solutions), of the corresponding system with constant inputs are derived.

**Authors:**V. Sree Hari Rao, Senior Member, IEEE , and P. Raja Sekhara Rao

**Published in:** 07-Feb-2013

Coronary heart disease (CHD) caused by hardening of artery walls due to cholesterol known as atherosclerosis is responsible for large number of deaths worldwide. The disease progression is slow, asymptomatic, and may lead to sudden cardiac arrest, stroke, or myocardial infraction. Presently, imaging techniques are being employed to understand the molecular and metabolic activity of atherosclerotic plaques to estimate the risk. Though imaging methods are able to provide some information on plaque metabolism, they lack the required resolution and sensitivity for detection.

**Authors:**V. Sree Hari Rao, Senior Member, IEEE , and M. Naresh Kumar

**Published in:** JANUARY 2013

As the global use of energy is projected to increase fivefold by 2100, several countries are investing in microalgal biotechnology as a source of renewable energy to enhance their energy security. Although microalgae are a source of high-value chemicals such as nutraceuticals and pharmaceuticals, with a gold-rush mentality many entrepreneurs focus primarily on biofuel as an end-product utilizing a few selected “traditional” algal species not native to the region, and extrapolate results obtained from controlled laboratory culture to large-scale outdoor production systems

**Authors:**V. Sree Hari Rao, Senior Member, IEEE , and Ravi V. Durvasula ,D.V. Subba Rao

**Published in:** 07-Feb-2013

Cardiovascular disease is a major health concern as more than 17.3 million deaths per year were reported as per the statistics of WHO report 2008 [54, 55]. The distribution of the deaths across the regions of the world is shown in Fig. 1. The cardiovascular disease caused by thickening of the walls of the arteries known as atherosclerosis has a long sub-clinical incubation period ranging from 30-50 years. The physicians would like to assess the risk of patients having a severe clinical event such as stroke or heart attack and predict the same if possible.

**Authors:**V. Sree Hari Rao, Senior Member, IEEE , and
M. Naresh Kumar

**Published in:** 2013

Avian Influenza, commonly known as Bird Flu, is an epidemic caused by H5N1 Virus That primarily affects birds such as chickens, wild water birds, ducks, and swans etc. On rare occasions, pigs and humans will also be affected with this virus.In recent years this epidemic has emerged as a major global health concern. The present chapter is aimed at developing mathematical models that predict the spread and outbreak diversity of low pathogenic avian influenza virus. Essentially, we present (i) a deterministic mathematical model which deals with the dynamics of human infection by avian influenza both in birds and in human, (ii) a one parameter model for spread of H5N1, and (iii) the statistical- transmission model of bird flu taking into account the factors that affecting the epidemic transmission such as source of infection, social and natural factors.

**Authors:**V. Sree Hari Rao, Senior Member, IEEE , and
Ranjit Kumar Upadhyay

**Published in:** 07-Feb-2013

Understanding the dynamics of an infectious disease holds the key for designing effective control strategies from public health perspective. There are two approaches for modeling the dynamics of epidemics namely (i) dynamical mathematical modeling (ii) incidence data modeling. Recent mathematical models are helpful in understanding the spread (transmission) of the infectious diseases. Incidence data reveals progressively the number of susceptible individuals turning into infectives when they come in contact with the infected individuals.

**Authors:**V. Sree Hari Rao, Senior Member, IEEE , and
M. Naresh Kumar

**Published in:** 2013

Dengue fever (DF) is a mosquito-borne infectious disease caused by the viruses of the genus Togaviridaesubgenus Flavirus. The disease has fi rst appeared in the Phillipines in 1953, and from then on it has become the most important anthropod-borne viral disease due to its spread among humans (Monath 1994) . The reemer-gence of this disease worldwide is causing larger, more frequent epidemics especially in cities and in the tropics.

**Authors:**V. Sree Hari Rao, Senior Member, IEEE , and
M. Naresh Kumar

**Published in:** 2013

A third-order system of ordinary differential equations, modeling two predators competing for a single prey species, is analyzed in this manuscript. A delay term modeling the delayed logistic growth of the prey is included. Fixed points of the system are identified, and a linearized stability analysis is carried out. For some parameter regime, there is a continuum of equilibria and these equilibria may undergo a zip bifurcation. The main results presented herein are that this zip bifurcation is “unsustainable” for certain ranges of values of the time delay parameter. Finally, spatial diffusion is incorporated in the delay differential equation model, and it is shown that the zip bifurcation remains unsustainable.

**Authors:**V. Sree Hari Rao, Senior Member, IEEE , and Jocirei D. Ferreira

**Published in:** 2013

Basel II allows banks to choose internal ratings based approach for credit risk estimation in addition to standardized approach. Credit estimation and bankruptcy prediction methods have been utilizing Altman’s z score method for the last several years. It is reported in many studies that z score is sensitive to changes in accounting figures. Researchers have proposed different variations to conventional z score that can improve the prediction accuracy. In this paper we develop a new multivariate non-linear model for computing the z score. In addition we develop a new credit risk index by fitting a Pearson type-III distribution to the transformed financial ratios. The results of our study have shown that the new z score can predict the bankruptcy with an accuracy of 98.6% as compared to 93.5% obtained by utilizing the Altman’s z score. Also, the discriminate analysis revealed that the new transformed financial ratios could predict the bankruptcy probability with an accuracy of 93.0% as compared to 87.4% using the weights of Altman’s z score.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE

**Published in:** 2013 - Under Review

Identification of the influential clinical symptoms and laboratory features that help in the diagnosis of dengue fever (DF) in early phase of the illness would aid in designing effective public health management and virological surveillance strategies. Keep-ing this as our main objective, we develop in this paper a new computational intelligence-based methodology that predicts the diagnosis in real time, minimizing the number of false positives and false negatives.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
Mallenahalli Naresh Kumar

**Published in:** 1, JANUARY 2012

Extraction of customer behavioral patterns is a complex task and widely studied for various industrial applications under different heading viz., customer retention management, business intelligence and data mining. In this paper, authors experimented to extract the behavioral patterns for customer retention in Health care insurance. Initially, the customers are classified into three general categories – stable, unstable and oscillatory.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
Murthy V.Jonnalagedda

**Published in:** 2012

Paratransgenesis is an approach to reducing vector competence using genetically modified symbionts. When applied to control of Chagas disease, the symbiont bacterium Rhodococcus rhodnii, resident in the gut lumen of the triatomine vector Rhodnius prolixus (Hemipetera: Reduviidae) is transformed to export cecropin A, an insect immune peptide. Cecropin A is active against Trypanosoma cruzi,the causative agent of Chagas disease.

**Authors:**V. Sree Hari Rao, Senior Member, IEEE and
S. Matthews
R.K. Sundaram
R.V. Durvasula

**Published in:** 2012

In this paper, activationdynamics of complex-valuedneural networks are studied on general time scales. Besides presenting conditions guaranteeing the existence of a unique equilibrium pattern, its global exponential stability is discussed. Some numerical examples for different time scales are given in order to highlight the results.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
Martin Bohner,
Suman Sanyal

**Published in:** 2012

In this paper we study the influence of weak Allee effection a predator-prey system model. This effect is included in the prey equation and we determine conditions for the occurrence of Hopf bifurcation. The stability properties of the system and the biological issues of the memory and Allee models on the coexistence of the two species are studied. Finally we present some simulations which allow one to verify the analytical conclusions obtained.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
Paulo C.C. TabareS,
JOCIREI D. FERREIRA

**Published in:** 2012

Several psychiatric conditions are associated with frequent fluc-tuations of mood. In this article, we discuss different techniques that are currently in use and suggest new techniques to evaluate such fluctuations. The main goal is to examine the usefulness of various measures to evaluate treatment effects or course of illness, especially in bipolar or unipolar affective illness to quantify mood fluctuations. We also point out some of the pitfalls in the quan-tification of these fluctuations and suggest novel mathematical models to better understand data obtained using different scales to quantify mood.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
Vikram K. Yeragani

**Published in:** 2012

A vector-borne disease is a consequence of an infection caused by a pathogenic microorganism transmitted by a vector (most commonly an arthropod), or occasionally, animals serving as intermediary hosts. The transmission dynamics depend on three factors: the pathogenic agent; the vectors; the human hosts and intermediary hosts such as domesticated and/or wild animals, which often serve as reservoirs for pathogens until susceptible human hosts are exposed

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
U. Surya Narayana Murthy

**Published in:** 2012

A model for the prediction of fatigue life based on the statistical distribution of pores, intermetallic particles and grains is presented here. This has been applied to a cast Al alloy A206 before and after friction stir processing (FSP). The model computes the probability of initiating a small crack based on the probability of finding combinations of defects and grains on the surface. Crack initiation and the propagation life of small cracks due to these defect and grain combinations are computed and summed to obtain the total fatigue life. The defect and grain combinations are ranked according to total fatigue life and the failure probability computed. Bending fatigue experiments were carried out on A206 before and after FSP. FSP eliminated the porosity, broke down the particles and refined the microstructure.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
R. Kapoor,
R.S. Mishra,
J.A. Baumann,
G. Grant,

**Published in:** 2012

In this paper, we propose a realistic mathematical model taking into account the mutual interference among the interacting populations. This model attempts to describe the control (vaccination) function as a function of the number of infective individuals, which is an improvement over the existing susceptibleinfective epidemic models. Regarding the growth of the epidemic as a nonlinear phenomenon we have developed a neural network architecture to estimate the vital parameters associated with this model. This architecture is based on a recently developed new class of neural networks known as co-operative and supportive neural networks.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
M. Naresh Kumar

**Published in:** 2012

Crude classification and false generalizations are the curse of organized life.’ However, that does not halt us from classifying objects and extending these generalizations to a vast category. Scientists have been classifying objects since time immemorial and this effort to group the objects so that they fit nicely together with other similar objects has led to the simplification and organization of an otherwise chaotic world. Classification in biology dates back to Aristotle’s time and has now reached such sophistication that human effort is often minimized and its place has been superseded by state -of-the-art computer-aided tools.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
Surya Narayana U Murthy

**Published in:** 2012

Weconsider a potential with two parameters, involving the amplitude and the scale, which adequately represent the real world phenomena concerning the receptor cells in a simple form. This potential also exhibits a sort of ``electrical neutrality'' making the total effect zero. Mathematically, this requires the potential V.x/ R D .x2 1/ exp.x2=2/, satisfy 1 1 V.x/dx D 0. It may be seen easily that the exponential decay makes the action of the potential local. This potential function, usually known as Inverted Mexican Hat potential, is found to closely approximate the functioning of bipolar cells in the retina, ion tunneling in ionic channels and also in other neuron cells.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
M.V. Altaisky

**Published in:** 2012

This article envisages development of global stability conditions for the basic chemostat model. Also the existence and uniqueness of solutions for the model equations are established for a general uptake function under conditions weaker than the Lipschitz condition. Comparisons are made with some existing results.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
P. Raja Sekhara Rao

**Published in:** 2012

We propose a new mathematical model for aquatic populations. This model incorporates mutual interference in all the three populations and an extra mortality term in zooplankton population and also taking into account the toxin liberation process of TPP population. The proposed model generalizes several other known models in the literature. The principal interest in this paper is in a numerical study of the model’s behaviour. It is observed that both types of food chains display same type of chaotic behaviour, short-term recurrent chaos, with different generating mechanisms. Toxin producing phytoplankton (TPP) reduces the grazing pressure of zooplankton. To observe the role of TPP, we consider Holling types I, II and III functional forms for this process. Our study suggests that toxic substances released by TPP population may act as bio-control by changing the state of chaos to order and extinction.

**Authors:**V. Sree Hari Rao, Senior Member, IEEE and
Ranjit Kumar Upadhyay

**Published in:** 2012

Avian influenza, commonly known as bird flu, is an epidemic caused by H5N1 virus that primarily affects birds like chickens, wild water birds, etc. On rare occasions, these can infect other species including pigs and humans. In the span of less than a year, the lethal strain of bird flu is spreading very fast across the globe mainly in South East Asia, parts of Central Asia, Africa and Europe. In order to study the patterns of spread of epidemic, we made an investigation of outbreaks of the epidemic in one week, that is from February 13–18, 2006, when the deadly virus surfaced in India.We have designed a statistical transmission model of bird flu taking into account the factors that affect the epidemic transmission such as source of infection, social and natural factors and various control measures are suggested.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
Ranjit Kumar Upadhyay,
Nitu Kumari

**Published in:** 2012

Complex valued neural networks (CVNNs for short) have been developed in recent years and their origin can be traced to (Aizenberg et al.1). The complex LMS algorithm formulated in Ref. 2 has been widely used in filtering theory. Subsequently CVNNs have been found useful in extending the scope of applications in optoelectronics, imaging, remote sensing, quantum neural devices and systems, spatiotemporal analysis of physiological neural devices and systems, and artificial neural information processing. A good account of the applications of these networks may be found in Hirose.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
Garimella Rama Murthy

**Published in:** 2012

In this article, we present a mathematical model of a unilingual society developing in to a bilingual society. We formulate, analyze the model and interpret the results of the analysis. The model is based on a two language policy motivated by the cultural and historical back ground of India.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
P. Raja Sekhara Rao

**Published in:** 2012

This Letter deals with the concepts of co-operation and support among neurons existing in a network which contribute to their collective capabilities and distributed operations. Activational dynamical properties of these networks are discussed.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
P. Raja Sekhara Rao

**Published in:** 2012

This paper deals with the problem of identification of unknown parameters and time-delay of dynamical systems. A polynomial function is employed to modify the structure of the system and subsequently suitable algorithms for identifying the parameters of time-lag systems are developed using neural networks. Illustrative examples for identification of time-lag systems and quasi-linear systems with lag have been presented. - 2006 Elsevier B.V. All rights reserved.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
N. Yadaiah
B.L. Deekshatulu
L. Sivakumar

**Published in:** 2012

Alimited nutrient consumer hybrid system which exhibits rich dynamics such as stability, instability and oscillatory characteristics is considered. The parameters that strongly influence the behavior of the system are identified and are estimated using the techniques of dynamic optimization. Two independent bio-control mechanisms are introduced into the system when the basic system exhibits instability characteristics. Values of the parameters representing these mechanisms are estimated at which the system stabilizes.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
P. Raja Sekhara Rao
K. Venkata Ratnam

**Published in:** 2012

In this paper we have analyzed a limited nutrient–consumer dynamic model involving distributed time delays both in material recycling and growth response of consumer. It is established that the system exhibits instability characteristics due to the presence of time delays. Three different types of naturally feasible bio-control mechanisms are proposed. It is established that these mechanisms have a stabilizing effect on the system in their own respect. Several independent sets of sufficient conditions for the global asymptotic stability are obtained in each case. Examples and simulations are provided for a clear understanding of the results.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
P. Raja Sekhara Rao

**Published in:** 2012

Several psychiatric conditions are associated with frequent fluctuations of affect. In this study, we propose a new technique to uniformly score depression and mania objectively and use a new mathematical technique to model the frequent fluctuations in mood using simulated data. Our main aim is to examine the usefulness of this measure for evaluating treatment effects or course of illness, especially in bipolar or unipolar affective illness to quantify mood fluctuations.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
C Raghvendra Rao
Vikram K Yeragani

**Published in:** 2012

A nutrient-consumer model involving a distributed delay in material recycling and a discrete delay in growth response has been analysed. Various easily verifiable sets of sufficient conditions for global asymptotic stability of the positive equilibrium solution of the model equations have been obtained and the length of the delay in each case has been estimated.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
P. RAJA SEKHARA RAO

**Published in:** 2012

Two models of ratio-dependent prey–predator dynamical systems are considered. Independent sets of sufficient conditions for global asymptotic stability of the positive equilibrium solution of the model equations in each case have been obtained. An example is provided for illustration and to compare with earlier results.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
P. Raja Sekhara Rao

**Published in:** 2012

Two models of ratio-dependent prey–predator dynamical systems are considered. Independent sets of sufficient conditions for global asymptotic stability of the positive equilibrium solution of the model equations in each case have been obtained. An example is provided for illustration and to compare with earlier results.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
Bh.R.M. Phaneendra

**Published in:** 2012

A mathematical model describing limited nutrient–consumer dynamics with both nutrient input and its supply rate varying with respect to time and involving distributed time delays both in nutrient recycling and biotic species growth has been analyzed. The existence of periodic solutions to the model equations when both the nutrient input and its supply rate are periodic, of the same period, has been established. Asymptotic behaviour of solutions of the model equations has also been discussed.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
P. Raja Sekhara Rao

**Published in:** 2012

In this paper we present the latest developments in the chemostat models involving time delays. The article envisages the development of a basic chemostat model into a model that explains the growth in a lake as well.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
P. Raja Sekhara Rao

**Published in:** 2012

This paper deals with the problem of identification of the unknown parameters of a dynamical system. Our work in this paper largely simulation related, follows the approach suggested by Kim and Lee [IEEE Int. Conf. Neural Networks (1993) 438–443] and it depends on the introduction of auxiliary polynomial. The merit of our work lies on the facts that no assumptions are placed on the stability of auxiliary polynomial and also that it does not require the a priori knowledge of the stability of the dynamical system, in question. Our method applies to both linear and quasi-linear dynamical systems. The results obtained involve the construction of appropriate neural networks. A variety of configurations of the dynamical systems are considered for simulation.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
Narri Yadaiah

**Published in:** 2012

A chemostat model with distributed time delays both in material recycling and biotic species growth has been considered. A concept of wall growth is introduced and its e/ect on the global stability of the positive equilibrium is discussed. Several easily veri1able independent sets of global stability conditions are presented.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
P. Raja Sekhara Rao

**Published in:** 2012

In this article viewing the subject of mathematical modelling as an art, several important features of this art have been presented in an artistic manner. Also, we discuss how to build mathematical models of some important real world problems.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE

**Published in:** 2012

This paper describes the neural net controller for dynamical systems. The main objective of the controller is to provide an appropriate input signal to a given physical process to yield desired response, besides rendering the unstable system becoming stable. A penality function defines the error term for the output layer neurons in the network for implementing back propagation algorithm.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
N. Yadaiah

**Published in:** 2012

A model for cellular neural networks involving time delays is considered. various sets if sufficient conditions, both delay dependent and independent, for the global asymptotic stability of the equilibrium solution are established. Asymptotic nature of solutions in the absence of an equilibrium solution is also discussed.

**Authors:**
V. Sree Hari Rao Senior Member, IEEE and
P. Raja Sekhara Rao

**Published in:** 2002

Interdisciplinary approaches provide solutions to the complex problems of modern society. It is important to observe that tools and techniques that are developed in one context may be applied in a variety of contexts. For example, techniques devel-oped to solve classical problems in the physical sciences can be extremely useful in the study of the biological, behavioral and life sciences.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
Vikram K. Yeragani

**Published in:** 2012

Mathematical models of food chains have been of interest in a number of recent papers. The models appearing in these papers are systems of three or more autonomous ordinary differential equations which satisfy dynamical systems hypothesis.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
L.H. Erbe,
H.I.Freedman

**Published in:** 2012

Interdisciplinary approaches provide solutions to the complex problems of modern society. It is important to observe that tools and techniques that are developed in one context may be applied in a variety of contexts. For example, techniques devel-oped to solve classical problems in the physical sciences can be extremely useful in the study of the biological, behavioral and life sciences.

**Authors:**
V. Sree Hari Rao, Senior Member, IEEE and
H.I. Freedman

**Published in:** 2012