INTERNATIONAL CONFERENCE ON ADVANCES IN MULTI-DISCIPLINARY SCIENCES AND ENGINEERING RESEARCH: ICAMSER-2021
A teacher, who is the provider of the proven educational knowledge, should be adequately competen... more A teacher, who is the provider of the proven educational knowledge, should be adequately competent in terms of expertise, trust, dedication, positive attitude, effective communication and patient listening. All these attributes can surely be inculcated in pupil teacher but only if the training is provided with maximum commitment, with specified objectives, taking into account the needs of todays' educational scenario and the needs of students. This paper emphasize on the system of training being provided to pre-service Mathematics' teachers, to develop their teaching skills. It includes the use of some creative teaching concepts to increase the interest, level of satisfaction and the outcome of their targeted Mathematics' students. Several studies, researches have shown that the students, who have been studying Mathematics since their childhood, are unable to perform simple calculations and are unable to solve simple numerical problem of their everyday life. This study will conclude with some suggestive facts that pre-service trainees should be trained in a way that other than the prescribed curriculum/syllabus, they should spend time to improve quantitative skills using some innovative techniques in regular class practice. As an example, the inventive methodology will also be discussed. And the second highlight will be the the emphasis on continual and rigorous assessment of the trainees during teaching practice, so that they can resolve the dearth and can go ahead with a handful of approaches to serve the purpose of fruitful teaching and learning.
INTERNATIONAL CONFERENCE ON ADVANCES IN MULTI-DISCIPLINARY SCIENCES AND ENGINEERING RESEARCH: ICAMSER-2021
In this paper, bibliometric analysis of scientific literature published during the period 1996-20... more In this paper, bibliometric analysis of scientific literature published during the period 1996-2020 in the field of Applied Mathematics has been presented using Scopus linked SCImago country ranking database. Further, India's contribution at global level is highlighted in particular using key bibliometric indicators namely document published, citations (external/self) and citations per document along with their annual corresponding growth to validate the findings. India is growing exponentially and contributing 2.5% to global research output with average 11.63% of annual corresponding growth. In addition, citations (external/self) and citations per document show average annual corresponding growth within ±5%. The outcomes of this study could foster new policies and the improvement in existing policies for various research activities especially for India.
As the trend towards E-teaching learning strengthens,questions remain unanswered with the effecti... more As the trend towards E-teaching learning strengthens,questions remain unanswered with the effectiveness of online learning in comparison to traditional classroom learning. The aim of this paper is to analyze the impact of online and offline (conventional method) teaching method on student's learning achievement. This article outlines a case study of E-teaching vs traditional teaching learning of a Mathematics course to first year engineering students within their respective programmes. The results of study are analyzed using bar/pie charts. Comparison between online teaching and traditional teaching has been done for various parameters related to students' interest for online/offline teaching, interaction with students, students' comfort level, instructor's competency etc. related to teaching and learning. The findings generate insights which help to understand the benefits and shortcomings of online/offline teaching consequently helping in improved design of such courses.
In this paper, A discrete-time food chain model of three species has been introduced comprising o... more In this paper, A discrete-time food chain model of three species has been introduced comprising of a set of three nonlinear difference equations. Evolutionary dynamics of this system have investigated and regular as well as chaotic attractors have been obtained for certain parameter values. Bifurcation diagrams have been drawn by varying parameters along coordinate axes and the motion has been analyzed. Numerical calculations have been carried out for calculations of Lyapunov exponents, topological entropies and correlation dimension. The investigation is then further extended to obtain FLI, SALI and DLI for regular and chaotic evolution of the food chain model.
The, "Complex systems", stands as a broad term for many diverse disciplines of science ... more The, "Complex systems", stands as a broad term for many diverse disciplines of science and engineering including natural & medical sciences. Complexities appearing in various dynamical systems during evolution are now interesting subjects of studies. Chaos appearing in various dynamical systems can also be viewed as a form of complexity. For some cases nonlinearities within the systems and for other cases piecewise continuity property of the system are responsible for such complexity. Dynamical systems represented by mathematical models having piecewise continuous properties show strange complexity character during evolution. Interesting recent articles explain widely on complexities in various systems. Observable quantities for complexity are measurement of Lyapunov exponents (LCEs), topological entropies, correlation dimension etc. The present article is related to study of complexity in systems having piecewise continuous properties. Some mathematical models are conside...
In this paper, A discrete-time food chain model of three species has been introduced comprising o... more In this paper, A discrete-time food chain model of three species has been introduced comprising of a set of three nonlinear difference equations. Evolutionary dynamics of this system have investigated and regular as well as chaotic attractors have been obtained for certain parameter values. Bifurcation diagrams have been drawn by varying parameters along coordinate axes and the motion has been analyzed. Numerical calculations have been carried out for calculations of Lyapunov exponents, topological entropies and correlation dimension. The investigation is then further extended to obtain FLI, SALI and DLI for regular and chaotic evolution of the food chain model.
Mathematical Journal of Interdisciplinary Sciences
The, "Complex systems", stands as a broad term for many diverse disciplines of science and engine... more The, "Complex systems", stands as a broad term for many diverse disciplines of science and engineering including natural & medical sciences. Complexities appearing in various dynamical systems during evolution are now interesting subjects of studies. Chaos appearing in various dynamical systems can also be viewed as a form of complexity. For some cases nonlinearities within the systems and for other cases piecewise continuity property of the system are responsible for such complexity. Dynamical systems represented by mathematical models having piecewise continuous properties show strange complexity character during evolution. Interesting recent articles explain widely on complexities in various systems. Observable quantities for complexity are measurement of Lyapunov exponents (LCEs), topological entropies, correlation dimension etc. The present article is related to study of complexity in systems having piecewise continuous properties. Some mathematical models are considered here in this regard including famous Lozi map, a discrete mathematical model and Chua circuit, a continuous model. Investigations have been carried forward to obtain various attractors of these maps appearing during evolution in diverse and interesting pattern for different set of values of parameters and for different initial conditions. Numerical investigations extended to obtain bifurcation diagrams, calculations of LCEs, topological entropies and correlation dimension together with their graphical representation.
Complex evolutionary behavior of an age-structured predator-prey threedimensional system has been... more Complex evolutionary behavior of an age-structured predator-prey threedimensional system has been investigated analytically as well as numerically. Natural populations, whose generations are non-overlapping, can be described by model of difference equations that explains how the populations evolve in discrete time steps. In this paper stability criteria of fixed points of 3-dimentional discrete model are discussed. Bifurcation diagrams of this map are drawn by varying one parameter while fixing value of other parameters. To examine complexity of the map during evolution, certain chaotic measures such as calculations of Lyapunov characteristic exponents (LCEs), topological entropies and correlation dimension have been done and represented graphically.
Complex evolutionary behavior of an age-structured predator-prey threedimensional system has been... more Complex evolutionary behavior of an age-structured predator-prey threedimensional system has been investigated analytically as well as numerically. Natural populations, whose generations are non-overlapping, can be described by model of difference equations that explains how the populations evolve in discrete time steps. In this paper stability criteria of fixed points of 3-dimentional discrete model are discussed. Bifurcation diagrams of this map are drawn by varying one parameter while fixing value of other parameters. To examine complexity of the map during evolution, certain chaotic measures such as calculations of Lyapunov characteristic exponents (LCEs), topological entropies and correlation dimension have been done and represented graphically. Mathematics Subject Classification: 34H10, 34C23, 37L30, 37B40
Asymptotic stability analysis applied to stabilize unstable fixed points and to control chaotic m... more Asymptotic stability analysis applied to stabilize unstable fixed points and to control chaotic motions in two and threedimensional discrete dynamical systems. A new set of parameter values obtained which stabilizes an unstable fixed point and control the chaotic evolution to regularity. The output of the considered model and that of the adjustable system continuously compared by a typical feedback and the difference used by the adaptation mechanism to modify the parameters. Suitable numerical simulation which are used thoroughly discussed and parameter values are adjusted. The findings are significant and interesting. This strategy has some advantages over many other chaos control methods in discrete systems but, however it can be applied within some limitations. KeywordsAsymptotic stability, Control parameter, Chaos, Lyapunov exponents.
195 Abstract—a discrete-time food chain model of three species, comprising of a set of three nonl... more 195 Abstract—a discrete-time food chain model of three species, comprising of a set of three nonlinear difference equations, has been considered. Bifurcation diagrams have been drawn by varying a system parameter along coordinate axes and the motion has been analyzed. Time series plots and phase plane attractor are drawn showing chaos in the system. In order to control the chaotic motion, certain periodic changes in the system parameter have been proposed for each equation. The system becomes regular with such a change in the model. Numerical calculations have been carried out for each case to obtain plots for Lyapunov exponents and topological entropy and also, correlation dimension for chaotic system has been obtained. The investigation is further extended to obtain DLI for regular and chaotic evolution of food chain model.
INTERNATIONAL CONFERENCE ON ADVANCES IN MULTI-DISCIPLINARY SCIENCES AND ENGINEERING RESEARCH: ICAMSER-2021
A teacher, who is the provider of the proven educational knowledge, should be adequately competen... more A teacher, who is the provider of the proven educational knowledge, should be adequately competent in terms of expertise, trust, dedication, positive attitude, effective communication and patient listening. All these attributes can surely be inculcated in pupil teacher but only if the training is provided with maximum commitment, with specified objectives, taking into account the needs of todays' educational scenario and the needs of students. This paper emphasize on the system of training being provided to pre-service Mathematics' teachers, to develop their teaching skills. It includes the use of some creative teaching concepts to increase the interest, level of satisfaction and the outcome of their targeted Mathematics' students. Several studies, researches have shown that the students, who have been studying Mathematics since their childhood, are unable to perform simple calculations and are unable to solve simple numerical problem of their everyday life. This study will conclude with some suggestive facts that pre-service trainees should be trained in a way that other than the prescribed curriculum/syllabus, they should spend time to improve quantitative skills using some innovative techniques in regular class practice. As an example, the inventive methodology will also be discussed. And the second highlight will be the the emphasis on continual and rigorous assessment of the trainees during teaching practice, so that they can resolve the dearth and can go ahead with a handful of approaches to serve the purpose of fruitful teaching and learning.
INTERNATIONAL CONFERENCE ON ADVANCES IN MULTI-DISCIPLINARY SCIENCES AND ENGINEERING RESEARCH: ICAMSER-2021
In this paper, bibliometric analysis of scientific literature published during the period 1996-20... more In this paper, bibliometric analysis of scientific literature published during the period 1996-2020 in the field of Applied Mathematics has been presented using Scopus linked SCImago country ranking database. Further, India's contribution at global level is highlighted in particular using key bibliometric indicators namely document published, citations (external/self) and citations per document along with their annual corresponding growth to validate the findings. India is growing exponentially and contributing 2.5% to global research output with average 11.63% of annual corresponding growth. In addition, citations (external/self) and citations per document show average annual corresponding growth within ±5%. The outcomes of this study could foster new policies and the improvement in existing policies for various research activities especially for India.
As the trend towards E-teaching learning strengthens,questions remain unanswered with the effecti... more As the trend towards E-teaching learning strengthens,questions remain unanswered with the effectiveness of online learning in comparison to traditional classroom learning. The aim of this paper is to analyze the impact of online and offline (conventional method) teaching method on student's learning achievement. This article outlines a case study of E-teaching vs traditional teaching learning of a Mathematics course to first year engineering students within their respective programmes. The results of study are analyzed using bar/pie charts. Comparison between online teaching and traditional teaching has been done for various parameters related to students' interest for online/offline teaching, interaction with students, students' comfort level, instructor's competency etc. related to teaching and learning. The findings generate insights which help to understand the benefits and shortcomings of online/offline teaching consequently helping in improved design of such courses.
In this paper, A discrete-time food chain model of three species has been introduced comprising o... more In this paper, A discrete-time food chain model of three species has been introduced comprising of a set of three nonlinear difference equations. Evolutionary dynamics of this system have investigated and regular as well as chaotic attractors have been obtained for certain parameter values. Bifurcation diagrams have been drawn by varying parameters along coordinate axes and the motion has been analyzed. Numerical calculations have been carried out for calculations of Lyapunov exponents, topological entropies and correlation dimension. The investigation is then further extended to obtain FLI, SALI and DLI for regular and chaotic evolution of the food chain model.
The, "Complex systems", stands as a broad term for many diverse disciplines of science ... more The, "Complex systems", stands as a broad term for many diverse disciplines of science and engineering including natural & medical sciences. Complexities appearing in various dynamical systems during evolution are now interesting subjects of studies. Chaos appearing in various dynamical systems can also be viewed as a form of complexity. For some cases nonlinearities within the systems and for other cases piecewise continuity property of the system are responsible for such complexity. Dynamical systems represented by mathematical models having piecewise continuous properties show strange complexity character during evolution. Interesting recent articles explain widely on complexities in various systems. Observable quantities for complexity are measurement of Lyapunov exponents (LCEs), topological entropies, correlation dimension etc. The present article is related to study of complexity in systems having piecewise continuous properties. Some mathematical models are conside...
In this paper, A discrete-time food chain model of three species has been introduced comprising o... more In this paper, A discrete-time food chain model of three species has been introduced comprising of a set of three nonlinear difference equations. Evolutionary dynamics of this system have investigated and regular as well as chaotic attractors have been obtained for certain parameter values. Bifurcation diagrams have been drawn by varying parameters along coordinate axes and the motion has been analyzed. Numerical calculations have been carried out for calculations of Lyapunov exponents, topological entropies and correlation dimension. The investigation is then further extended to obtain FLI, SALI and DLI for regular and chaotic evolution of the food chain model.
Mathematical Journal of Interdisciplinary Sciences
The, "Complex systems", stands as a broad term for many diverse disciplines of science and engine... more The, "Complex systems", stands as a broad term for many diverse disciplines of science and engineering including natural & medical sciences. Complexities appearing in various dynamical systems during evolution are now interesting subjects of studies. Chaos appearing in various dynamical systems can also be viewed as a form of complexity. For some cases nonlinearities within the systems and for other cases piecewise continuity property of the system are responsible for such complexity. Dynamical systems represented by mathematical models having piecewise continuous properties show strange complexity character during evolution. Interesting recent articles explain widely on complexities in various systems. Observable quantities for complexity are measurement of Lyapunov exponents (LCEs), topological entropies, correlation dimension etc. The present article is related to study of complexity in systems having piecewise continuous properties. Some mathematical models are considered here in this regard including famous Lozi map, a discrete mathematical model and Chua circuit, a continuous model. Investigations have been carried forward to obtain various attractors of these maps appearing during evolution in diverse and interesting pattern for different set of values of parameters and for different initial conditions. Numerical investigations extended to obtain bifurcation diagrams, calculations of LCEs, topological entropies and correlation dimension together with their graphical representation.
Complex evolutionary behavior of an age-structured predator-prey threedimensional system has been... more Complex evolutionary behavior of an age-structured predator-prey threedimensional system has been investigated analytically as well as numerically. Natural populations, whose generations are non-overlapping, can be described by model of difference equations that explains how the populations evolve in discrete time steps. In this paper stability criteria of fixed points of 3-dimentional discrete model are discussed. Bifurcation diagrams of this map are drawn by varying one parameter while fixing value of other parameters. To examine complexity of the map during evolution, certain chaotic measures such as calculations of Lyapunov characteristic exponents (LCEs), topological entropies and correlation dimension have been done and represented graphically.
Complex evolutionary behavior of an age-structured predator-prey threedimensional system has been... more Complex evolutionary behavior of an age-structured predator-prey threedimensional system has been investigated analytically as well as numerically. Natural populations, whose generations are non-overlapping, can be described by model of difference equations that explains how the populations evolve in discrete time steps. In this paper stability criteria of fixed points of 3-dimentional discrete model are discussed. Bifurcation diagrams of this map are drawn by varying one parameter while fixing value of other parameters. To examine complexity of the map during evolution, certain chaotic measures such as calculations of Lyapunov characteristic exponents (LCEs), topological entropies and correlation dimension have been done and represented graphically. Mathematics Subject Classification: 34H10, 34C23, 37L30, 37B40
Asymptotic stability analysis applied to stabilize unstable fixed points and to control chaotic m... more Asymptotic stability analysis applied to stabilize unstable fixed points and to control chaotic motions in two and threedimensional discrete dynamical systems. A new set of parameter values obtained which stabilizes an unstable fixed point and control the chaotic evolution to regularity. The output of the considered model and that of the adjustable system continuously compared by a typical feedback and the difference used by the adaptation mechanism to modify the parameters. Suitable numerical simulation which are used thoroughly discussed and parameter values are adjusted. The findings are significant and interesting. This strategy has some advantages over many other chaos control methods in discrete systems but, however it can be applied within some limitations. KeywordsAsymptotic stability, Control parameter, Chaos, Lyapunov exponents.
195 Abstract—a discrete-time food chain model of three species, comprising of a set of three nonl... more 195 Abstract—a discrete-time food chain model of three species, comprising of a set of three nonlinear difference equations, has been considered. Bifurcation diagrams have been drawn by varying a system parameter along coordinate axes and the motion has been analyzed. Time series plots and phase plane attractor are drawn showing chaos in the system. In order to control the chaotic motion, certain periodic changes in the system parameter have been proposed for each equation. The system becomes regular with such a change in the model. Numerical calculations have been carried out for each case to obtain plots for Lyapunov exponents and topological entropy and also, correlation dimension for chaotic system has been obtained. The investigation is further extended to obtain DLI for regular and chaotic evolution of food chain model.
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