Preface |
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vii | |
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1 Dissipative Dynamical Systems |
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1 | (42) |
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1.1 Limit Sets and Global Attractors |
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2 | (7) |
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1.2 Chain Transitivity and Attractivity |
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9 | (10) |
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1.2.1 Chain Transitive Sets |
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9 | (7) |
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1.2.2 Attractivity and Morse Decompositions |
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16 | (3) |
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1.3 Strong Repellers and Uniform Persistence |
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19 | (14) |
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20 | (3) |
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1.3.2 Uniform Persistence |
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23 | (3) |
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1.3.3 Persistence and Attractors |
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26 | (3) |
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29 | (4) |
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1.4 Persistence Under Perturbations |
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33 | (7) |
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1.4.1 Perturbation of a Globally Stable Steady State |
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33 | (1) |
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1.4.2 Persistence Uniform in Parameters |
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34 | (1) |
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35 | (5) |
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40 | (3) |
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43 | (34) |
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2.1 Attracting Order Intervals and Connecting Orbits |
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44 | (4) |
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2.2 Global Attractivity and Convergence |
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48 | (4) |
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2.3 Subhomogeneous Maps and Skew-Product Semiflows |
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52 | (7) |
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2.4 Competitive Systems on Ordered Banach Spaces |
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59 | (3) |
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2.5 Saddle Point Behavior |
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62 | (7) |
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2.6 Exponential Ordering Induced Monotonicity |
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69 | (4) |
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73 | (4) |
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3 Nonautonomous Semiflows |
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77 | (42) |
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78 | (9) |
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3.1.1 Reduction to Poincare Maps |
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78 | (2) |
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3.1.2 Monotone Periodic Systems |
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80 | (7) |
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3.2 Asymptotically Periodic Semiflows |
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87 | (11) |
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3.2.1 Reduction to Asymptotically Autonomous Processes |
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88 | (2) |
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3.2.2 Asymptotically Periodic Systems |
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90 | (8) |
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3.3 Monotone and Subhomogeneous Almost Periodic Systems |
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98 | (9) |
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107 | (5) |
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3.5 Abstract Nonautonomous FDEs |
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112 | (4) |
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116 | (3) |
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4 A Discrete-Time Chemostat Model |
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119 | (12) |
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120 | (2) |
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122 | (3) |
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125 | (3) |
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128 | (3) |
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5 N-Species Competition in a Periodic Chemostat |
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131 | (24) |
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5.1 Weak Periodic Repellers |
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132 | (3) |
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5.2 Single Population Growth |
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135 | (7) |
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5.3 N-Species Competition |
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142 | (5) |
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5.4 3-Species Competition |
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147 | (5) |
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152 | (3) |
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6 Almost Periodic Competitive Systems |
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155 | (26) |
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6.1 Almost Periodic Attractors in Scalar Equations |
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156 | (9) |
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6.2 Competitive Coexistence |
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165 | (4) |
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6.3 An Almost Periodic Chemostat Model |
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169 | (5) |
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6.4 Nonautonomous 2-Species Competitive Systems |
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174 | (6) |
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180 | (1) |
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7 Competitor--Competitor--Mutualist Systems |
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181 | (32) |
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7.1 Weak Periodic Repellers |
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183 | (2) |
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7.2 Competitive Coexistence |
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185 | (9) |
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7.3 Competitive Exclusion |
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194 | (3) |
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7.4 Bifurcations of Periodic Solutions: A Case Study |
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197 | (13) |
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210 | (3) |
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8 A Periodically Pulsed Bioreactor Model |
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213 | (28) |
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214 | (3) |
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217 | (11) |
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8.2.1 Conservation Principle |
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218 | (1) |
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8.2.2 Single Species Growth |
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219 | (5) |
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8.2.3 Two-Species Competition |
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224 | (4) |
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228 | (11) |
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8.3.1 Periodic Systems with Parameters |
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229 | (3) |
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8.3.2 Single Species Growth |
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232 | (4) |
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8.3.3 Two-Species Competition |
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236 | (3) |
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239 | (2) |
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9 A Nonlocal and Delayed Predator--Prey Model |
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241 | (24) |
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242 | (5) |
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247 | (3) |
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250 | (2) |
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9.4 Global Attractivity: A Fluctuation Method |
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252 | (3) |
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9.5 Threshold Dynamics: A Single Species Model |
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255 | (8) |
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263 | (2) |
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10 Traveling Waves in Bistable Nonlinearities |
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265 | (20) |
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10.1 Existence of Periodic Traveling Waves |
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266 | (6) |
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10.2 Attractivity and Uniqueness of Traveling Waves |
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272 | (5) |
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10.3 Exponential Stability of Traveling Waves |
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277 | (4) |
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10.4 Autonomous Case: A Spruce Budworm Model |
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281 | (2) |
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283 | (2) |
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11 The Theory of Basic Reproduction Ratios |
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285 | (32) |
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11.1 Periodic Systems with Time Delay |
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286 | (11) |
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11.2 A Periodic SEIR Model |
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297 | (5) |
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11.3 Reaction--Diffusion Systems |
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302 | (7) |
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11.4 A Spatial Model of Rabies |
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309 | (6) |
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315 | (2) |
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12 A Population Model with Periodic Delay |
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317 | (20) |
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318 | (4) |
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322 | (11) |
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12.3 Numerical Computation of R0 |
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333 | (3) |
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336 | (1) |
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13 A Periodic Reaction--Diffusion SIS Model |
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337 | (24) |
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13.1 Basic Reproduction Ratio |
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339 | (10) |
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349 | (5) |
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354 | (4) |
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358 | (1) |
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359 | (2) |
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14 A Nonlocal Spatial Model for Lyme Disease |
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361 | (24) |
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362 | (3) |
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14.2 Disease-Free Dynamics |
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365 | (8) |
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373 | (11) |
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384 | (1) |
References |
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385 | (26) |
Index |
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411 | |