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E-grāmata: Dynamical Systems in Population Biology

  • Formāts: EPUB+DRM
  • Sērija : CMS Books in Mathematics
  • Izdošanas datums: 11-Apr-2017
  • Izdevniecība: Springer International Publishing AG
  • Valoda: eng
  • ISBN-13: 9783319564333
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  • Formāts: EPUB+DRM
  • Sērija : CMS Books in Mathematics
  • Izdošanas datums: 11-Apr-2017
  • Izdevniecība: Springer International Publishing AG
  • Valoda: eng
  • ISBN-13: 9783319564333

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This research monograph provides an introduction to the theory of nonautonomous semiflows with applications to population dynamics. It develops dynamical system approaches to various evolutionary equations such as difference, ordinary, functional, and partial differential equations, and pays more attention to periodic and almost periodic phenomena. The presentation includes persistence theory, monotone dynamics, periodic and almost periodic semiflows, basic reproduction ratios, traveling waves, and global analysis of prototypical population models in ecology and epidemiology. 

Research mathematicians working with nonlinear dynamics, particularly those interested in applications to biology, will find this book useful. It may also be used as a textbook or as supplementary reading for a graduate special topics course on the theory and applications of dynamical systems.





Dr. Xiao-Qiang Zhao is a University Research Professor at Memorial University of Newfoundland, Canada. His main research interests involve applied dynamical systems, nonlinear differential equations, and mathematical biology. He is the author of more than 100 papers, and his research has played an important role in the development of the theory and applications of monotone dynamical systems, periodic and almost periodic semiflows, uniform persistence, and basic reproduction ratios.

Recenzijas

In this interesting book an introduction to the theory of nonautonomous semiows on metric spaces is presented and several applications to population dynamics are given. More attention is paid to periodic and almost periodic models. The mathematician interested in mathematical biology will find this book useful. It may be used as a supplementary textbook for graduate topics related to applications of dynamical systems on mathematical biology. The book includes an impressive list of references. (George Karakostas, zbMATH 13.93.37.003, 2018)

Preface vii
1 Dissipative Dynamical Systems
1(42)
1.1 Limit Sets and Global Attractors
2(7)
1.2 Chain Transitivity and Attractivity
9(10)
1.2.1 Chain Transitive Sets
9(7)
1.2.2 Attractivity and Morse Decompositions
16(3)
1.3 Strong Repellers and Uniform Persistence
19(14)
1.3.1 Strong Repellers
20(3)
1.3.2 Uniform Persistence
23(3)
1.3.3 Persistence and Attractors
26(3)
1.3.4 Coexistence States
29(4)
1.4 Persistence Under Perturbations
33(7)
1.4.1 Perturbation of a Globally Stable Steady State
33(1)
1.4.2 Persistence Uniform in Parameters
34(1)
1.4.3 Robust Permanence
35(5)
1.5 Notes
40(3)
2 Monotone Dynamics
43(34)
2.1 Attracting Order Intervals and Connecting Orbits
44(4)
2.2 Global Attractivity and Convergence
48(4)
2.3 Subhomogeneous Maps and Skew-Product Semiflows
52(7)
2.4 Competitive Systems on Ordered Banach Spaces
59(3)
2.5 Saddle Point Behavior
62(7)
2.6 Exponential Ordering Induced Monotonicity
69(4)
2.7 Notes
73(4)
3 Nonautonomous Semiflows
77(42)
3.1 Periodic Semiflows
78(9)
3.1.1 Reduction to Poincare Maps
78(2)
3.1.2 Monotone Periodic Systems
80(7)
3.2 Asymptotically Periodic Semiflows
87(11)
3.2.1 Reduction to Asymptotically Autonomous Processes
88(2)
3.2.2 Asymptotically Periodic Systems
90(8)
3.3 Monotone and Subhomogeneous Almost Periodic Systems
98(9)
3.4 Continuous Processes
107(5)
3.5 Abstract Nonautonomous FDEs
112(4)
3.6 Notes
116(3)
4 A Discrete-Time Chemostat Model
119(12)
4.1 The Model
120(2)
4.2 The Limiting System
122(3)
4.3 Global Dynamics
125(3)
4.4 Notes
128(3)
5 N-Species Competition in a Periodic Chemostat
131(24)
5.1 Weak Periodic Repellers
132(3)
5.2 Single Population Growth
135(7)
5.3 N-Species Competition
142(5)
5.4 3-Species Competition
147(5)
5.5 Notes
152(3)
6 Almost Periodic Competitive Systems
155(26)
6.1 Almost Periodic Attractors in Scalar Equations
156(9)
6.2 Competitive Coexistence
165(4)
6.3 An Almost Periodic Chemostat Model
169(5)
6.4 Nonautonomous 2-Species Competitive Systems
174(6)
6.5 Notes
180(1)
7 Competitor--Competitor--Mutualist Systems
181(32)
7.1 Weak Periodic Repellers
183(2)
7.2 Competitive Coexistence
185(9)
7.3 Competitive Exclusion
194(3)
7.4 Bifurcations of Periodic Solutions: A Case Study
197(13)
7.5 Notes
210(3)
8 A Periodically Pulsed Bioreactor Model
213(28)
8.1 The Model
214(3)
8.2 Unperturbed Model
217(11)
8.2.1 Conservation Principle
218(1)
8.2.2 Single Species Growth
219(5)
8.2.3 Two-Species Competition
224(4)
8.3 Perturbed Model
228(11)
8.3.1 Periodic Systems with Parameters
229(3)
8.3.2 Single Species Growth
232(4)
8.3.3 Two-Species Competition
236(3)
8.4 Notes
239(2)
9 A Nonlocal and Delayed Predator--Prey Model
241(24)
9.1 The Model
242(5)
9.2 Global Coexistence
247(3)
9.3 Global Extinction
250(2)
9.4 Global Attractivity: A Fluctuation Method
252(3)
9.5 Threshold Dynamics: A Single Species Model
255(8)
9.6 Notes
263(2)
10 Traveling Waves in Bistable Nonlinearities
265(20)
10.1 Existence of Periodic Traveling Waves
266(6)
10.2 Attractivity and Uniqueness of Traveling Waves
272(5)
10.3 Exponential Stability of Traveling Waves
277(4)
10.4 Autonomous Case: A Spruce Budworm Model
281(2)
10.5 Notes
283(2)
11 The Theory of Basic Reproduction Ratios
285(32)
11.1 Periodic Systems with Time Delay
286(11)
11.2 A Periodic SEIR Model
297(5)
11.3 Reaction--Diffusion Systems
302(7)
11.4 A Spatial Model of Rabies
309(6)
11.5 Notes
315(2)
12 A Population Model with Periodic Delay
317(20)
12.1 Model Formulation
318(4)
12.2 Threshold Dynamics
322(11)
12.3 Numerical Computation of R0
333(3)
12.4 Notes
336(1)
13 A Periodic Reaction--Diffusion SIS Model
337(24)
13.1 Basic Reproduction Ratio
339(10)
13.2 Threshold Dynamics
349(5)
13.3 Global Attractivity
354(4)
13.4 Discussion
358(1)
13.5 Notes
359(2)
14 A Nonlocal Spatial Model for Lyme Disease
361(24)
14.1 The Model
362(3)
14.2 Disease-Free Dynamics
365(8)
14.3 Global Dynamics
373(11)
14.4 Notes
384(1)
References 385(26)
Index 411
Dr. Xiao-Qiang Zhao is a professor in applied mathematics at Memorial University of Newfoundland, Canada. His main research interests involve applied dynamical systems, nonlinear differential equations, and mathematical biology. He is the author of more than 40 papers and his research has played an important role in the development of the theory of periodic and almost periodic semiflows and their applications.