Ebook: The Logistic Map and the Route to Chaos: From The Beginnings to Modern Applications
- Tags: Complexity, Applications of Mathematics
- Series: Understanding Complex Systems
- Year: 2006
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
Pierre-Francois Verhulst, with his seminal work using the logistic map to describe population growth and saturation, paved the way for the many applications of this tool in modern mathematics, physics, chemistry, biology, economics and sociology. Indeed nowadays the logistic map is considered a useful and paradigmatic showcase for the route leading to chaos. This volume gathers contributions from some of the leading specialists in the field to present a state-of-the art view of the many ramifications of the developments initiated by Verhulst over a century ago.
Pierre-Francois Verhulst, with his seminal work using the logistic map to describe population growth and saturation, paved the way for the many applications of this tool in modern mathematics, physics, chemistry, biology, economics and sociology. Indeed nowadays the logistic map is considered a useful and paradigmatic showcase for the route leading to chaos. This volume gathers contributions from some of the leading specialists in the field to present a state-of-the art view of the many ramifications of the developments initiated by Verhulst over a century ago.
Pierre-Francois Verhulst, with his seminal work using the logistic map to describe population growth and saturation, paved the way for the many applications of this tool in modern mathematics, physics, chemistry, biology, economics and sociology. Indeed nowadays the logistic map is considered a useful and paradigmatic showcase for the route leading to chaos. This volume gathers contributions from some of the leading specialists in the field to present a state-of-the art view of the many ramifications of the developments initiated by Verhulst over a century ago.
Content:
Front Matter....Pages I-XX
Front Matter....Pages 1-1
Chaotic Growth with the Logistic Model of P.-F. Verhulst....Pages 3-11
Pierre-Fran?ois Verhulst’s Final Triumph....Pages 13-28
Limits to Success. The Iron Law of Verhulst....Pages 29-51
Recurrent Generation of Verhulst Chaos Maps at Any Order and Their Stabilization Diagram by Anticipative Control....Pages 53-75
Coherence in Complex Networks of Oscillators....Pages 77-97
Growth of Random Sequences....Pages 99-113
Front Matter....Pages 115-115
Logistic Population Growth and Beyond: The Influence of Advection and Nonlocal Effects....Pages 117-129
Predator-Prey Encounters Studied as Relative Particle Diffusion....Pages 131-146
Extinction Dynamics in Lotka-Volterra Ecosystems on Evolving Networks....Pages 147-159
Exact Law of Live Nature....Pages 161-173
Manifestation of Chaos in Real Complex Systems: Case of Parkinson’s Disease....Pages 175-196
Monte Carlo Simulations of Ageing and Speciation....Pages 197-219
Front Matter....Pages 221-221
Influence of Information Flow in the Formation of Economic Cycles....Pages 223-238
Logistic Function in Large Financial Crashes....Pages 239-258
Agent Based Approaches to Income Distributions and the Impact of Memory....Pages 259-272
Front Matter....Pages 273-273
Agglomeration/Aggregation and Chaotic Behaviour in d-Dimensional Spatio-Temporal Matter Rearrangements Number-Theoretic Aspects....Pages 275-294
A Chaos and Fractal Dynamic Approach to the Fracture Mechanics....Pages 295-316
Nonlinear Dynamics and Fractal Avalanches in a Pile of Rice....Pages 317-335
Front Matter....Pages 337-337
A Recent Appreciation of the Singular Dynamics at the Edge of Chaos....Pages 339-354
Quantum Chaos Versus Classical Chaos: Why is Quantum Chaos Weaker?....Pages 355-367
Front Matter....Pages 337-337
On the Prediction of Chaos in the Restricted Three-Body Problem....Pages 369-383
Order and Chaos in Some Hamiltonian Systems of Interest in Plasma Physics....Pages 385-405
Back Matter....Pages 407-413
Pierre-Francois Verhulst, with his seminal work using the logistic map to describe population growth and saturation, paved the way for the many applications of this tool in modern mathematics, physics, chemistry, biology, economics and sociology. Indeed nowadays the logistic map is considered a useful and paradigmatic showcase for the route leading to chaos. This volume gathers contributions from some of the leading specialists in the field to present a state-of-the art view of the many ramifications of the developments initiated by Verhulst over a century ago.
Content:
Front Matter....Pages I-XX
Front Matter....Pages 1-1
Chaotic Growth with the Logistic Model of P.-F. Verhulst....Pages 3-11
Pierre-Fran?ois Verhulst’s Final Triumph....Pages 13-28
Limits to Success. The Iron Law of Verhulst....Pages 29-51
Recurrent Generation of Verhulst Chaos Maps at Any Order and Their Stabilization Diagram by Anticipative Control....Pages 53-75
Coherence in Complex Networks of Oscillators....Pages 77-97
Growth of Random Sequences....Pages 99-113
Front Matter....Pages 115-115
Logistic Population Growth and Beyond: The Influence of Advection and Nonlocal Effects....Pages 117-129
Predator-Prey Encounters Studied as Relative Particle Diffusion....Pages 131-146
Extinction Dynamics in Lotka-Volterra Ecosystems on Evolving Networks....Pages 147-159
Exact Law of Live Nature....Pages 161-173
Manifestation of Chaos in Real Complex Systems: Case of Parkinson’s Disease....Pages 175-196
Monte Carlo Simulations of Ageing and Speciation....Pages 197-219
Front Matter....Pages 221-221
Influence of Information Flow in the Formation of Economic Cycles....Pages 223-238
Logistic Function in Large Financial Crashes....Pages 239-258
Agent Based Approaches to Income Distributions and the Impact of Memory....Pages 259-272
Front Matter....Pages 273-273
Agglomeration/Aggregation and Chaotic Behaviour in d-Dimensional Spatio-Temporal Matter Rearrangements Number-Theoretic Aspects....Pages 275-294
A Chaos and Fractal Dynamic Approach to the Fracture Mechanics....Pages 295-316
Nonlinear Dynamics and Fractal Avalanches in a Pile of Rice....Pages 317-335
Front Matter....Pages 337-337
A Recent Appreciation of the Singular Dynamics at the Edge of Chaos....Pages 339-354
Quantum Chaos Versus Classical Chaos: Why is Quantum Chaos Weaker?....Pages 355-367
Front Matter....Pages 337-337
On the Prediction of Chaos in the Restricted Three-Body Problem....Pages 369-383
Order and Chaos in Some Hamiltonian Systems of Interest in Plasma Physics....Pages 385-405
Back Matter....Pages 407-413
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