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Environmental variation plays an important role in many biological and ecological dynamical systems. This monograph focuses on the study of oscillation and the stability of delay models occurring in biology. The book presents recent research results on the qualitative behavior of mathematical models under different physical and environmental conditions, covering dynamics including the distribution and consumption of food. Researchers in the fields of mathematical modeling, mathematical biology, and population dynamics will be particularly interested in this material.
List of contents
1. Logistic Models.- 2. Oscillation of Delay Logistic Models.- 3. Stability of Delay Logistic Models.- 4. Logistic Models with Piecewise Arguments.- 5. Food-Limited Population Models.- 6. Logistic Models with Diffusions.
About the author
Sumati Kumari Panda, Ph.D., is a Professor of Mathematics at the GMR Institute of Technology, India. Her research areas include fractional calculus, fixed point theory, neural networks, and their applications. She has published more than 100 research papers in reputed international journals and presented her work at several national and international conferences. She is currently serving as an Academic Editor for Scientific Reports (Springer, Scopus & SCIE-indexed). Dr. Panda received her Ph.D. in Mathematics from K.L. University in 2015.
Velusamy Vijayakumar, Ph.D., is an Assistant Professor at the Vellore Institute of Technology (VIT), Vellore, India. His research interests include fractional calculus, dynamical systems, mathematical control theory, and neural networks. Dr. Vijayakumar has authored over 220 research articles in reputed scientific journals. Dr. Vijayakumar received his B.Sc, M.Sc, M.Phil, and Ph.D. degrees in Mathematics from Bharathiar University, Coimbatore, Tamil Nadu, India, in 2002, 2004, 2006, and 2016 respectively.
Ravi P. Agarwal, Ph.D., is an Emeritus Research Professor in the Department of Mathematics and Systems Engineering at the Florida Institute of Technology (USA). He has authored or co-authored more than 50 books and more than 2,000 research articles. He has received numerus honors and awards from several universities of the world. His research interests include nonlinear analysis, differential and difference equations, fixed point theory, and general inequalities. Dr. Agarwal received his Ph.D. at the Indian Institute of Technology, Madras, India, in 1973.
Summary
Environmental variation plays an important role in many biological and ecological dynamical systems. This monograph focuses on the study of oscillation and the stability of delay models occurring in biology. The book presents recent research results on the qualitative behavior of mathematical models under different physical and environmental conditions, covering dynamics including the distribution and consumption of food. Researchers in the fields of mathematical modeling, mathematical biology, and population dynamics will be particularly interested in this material.
Additional text
“The text under review collects under a single cover a number of important theoretical results on delay differential equations, both ordinary and partial; these results can be applied for the analysis of relevant mathematical models of population dynamics. … This text is a valuable resource for researchers and graduate students in mathematics who study stability properties and oscillation of solutions for various classes of delay differential equations; it contains many useful mathematical results and a rich list of references.” (Svitlana P. Rogovchenko, Mathematical Reviews, February, 2016)
“This book concerns the behaviour of a particular class of delay differential equations … . The book should be of interest to those interested in proving results about the behaviour of delay differential equations.” (Carlo Laing, zbMATH 1312.37001,2015)
Report
"The text under review collects under a single cover a number of important theoretical results on delay differential equations, both ordinary and partial; these results can be applied for the analysis of relevant mathematical models of population dynamics. ... This text is a valuable resource for researchers and graduate students in mathematics who study stability properties and oscillation of solutions for various classes of delay differential equations; it contains many useful mathematical results and a rich list of references." (Svitlana P. Rogovchenko, Mathematical Reviews, February, 2016)
"This book concerns the behaviour of a particular class of delay differential equations ... . The book should be of interest to those interested in proving results about the behaviour of delay differential equations." (Carlo Laing, zbMATH 1312.37001,2015)
