Evidence of chaos in eco-epidemic models.
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[1] A. J. Hendriks,et al. Allometric scaling of rate, age and density parameters in ecological models , 1999 .
[2] Pejman Rohani,et al. Persistence, chaos and synchrony in ecology and epidemiology , 1998, Proceedings of the Royal Society of London. Series B: Biological Sciences.
[3] R. May,et al. Population Biology of Infectious Diseases , 1982, Dahlem Workshop Reports.
[4] Ezio Venturino,et al. The Influence of Diseases on Lotka-Volterra Systems , 1993 .
[5] Joydev Chattopadhyay,et al. Infection in prey population may act as a biological control in ratio-dependent predator?prey models , 2004 .
[6] H. Hethcote,et al. Competing species models with an infectious disease. , 2005, Mathematical biosciences and engineering : MBE.
[7] A A Berryman,et al. Are ecological systems chaotic - And if not, why not? , 1989, Trends in ecology & evolution.
[8] R M May,et al. The invasion, persistence and spread of infectious diseases within animal and plant communities. , 1986, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.
[9] M. Rosenzweig. Paradox of Enrichment: Destabilization of Exploitation Ecosystems in Ecological Time , 1971, Science.
[10] R. Macarthur,et al. Graphical Representation and Stability Conditions of Predator-Prey Interactions , 1963, The American Naturalist.
[11] Hopf Bifurcation Analysis of Pathogen-Immune Interaction Dynamics With Delay Kernel , 2006, math/0610690.
[12] Rongsong Liu,et al. Spread Pattern Formation of H5N1-Avian Influenza and its Implications for Control Strategies , 2008 .
[13] R. May,et al. Population biology of infectious diseases: Part II , 1979, Nature.
[14] J. Chattopadhyay,et al. Role of horizontal incidence in the occurrence and control of chaos in an eco-epidemiological system. , 2007, Mathematical medicine and biology : a journal of the IMA.
[15] Thilo Gross,et al. Analytical search for bifurcation surfaces in parameter space , 2004 .
[16] Shigui Ruan,et al. Global analysis of an epidemic model with nonmonotone incidence rate , 2006, Mathematical Biosciences.
[17] Adam Kleczkowski,et al. Seasonality and extinction in chaotic metapopulations , 1995, Proceedings of the Royal Society of London. Series B: Biological Sciences.
[18] Zhien Ma,et al. A predator-prey model with infected prey. , 2004, Theoretical population biology.
[19] Mercedes Pascual,et al. Diffusion-induced chaos in a spatial predator–prey system , 1993, Proceedings of the Royal Society of London. Series B: Biological Sciences.
[20] Marten Scheffer,et al. Chaos in a long-term experiment with a plankton community , 2008, Nature.
[21] Herbert W. Hethcote,et al. The Mathematics of Infectious Diseases , 2000, SIAM Rev..
[22] H. I. Freedman,et al. Predator-prey populations with parasitic infection , 1989, Journal of mathematical biology.
[23] Thilo Gross,et al. Enrichment and foodchain stability: the impact of different forms of predator-prey interaction. , 2004, Journal of theoretical biology.
[24] John F. Andrews,et al. A mathematical model for the continuous culture of microorganisms utilizing inhibitory substrates , 1968 .
[25] G. Ruxton,et al. Population Floors and the Persistence of Chaos in Ecological Models. , 1998, Theoretical population biology.
[26] Donald L. DeAngelis,et al. A Model for Tropic Interaction , 1975 .
[27] Graeme D. Ruxton,et al. Low levels of immigration between chaotic populations can reduce system extinctions by inducing asynchronous regular cycles , 1994, Proceedings of the Royal Society of London. Series B: Biological Sciences.
[28] F. Hilker,et al. Disease-induced stabilization of predator-prey oscillations. , 2008, Journal of theoretical biology.
[29] S. Ellner,et al. Chaos in Ecology: Is Mother Nature a Strange Attractor?* , 1993 .
[30] J. Yorke,et al. Recurrent outbreaks of measles, chickenpox and mumps. II. Systematic differences in contact rates and stochastic effects. , 1973, American journal of epidemiology.
[31] Joydev Chattopadhyay,et al. A predator—prey model with disease in the prey , 1999 .
[32] Roy M. Anderson,et al. Transmission dynamics of HIV infection , 1987, Nature.
[33] G S Wolkowicz,et al. Predator-prey systems with group defence: The paradox of enrichment revisited , 1986, Bulletin of mathematical biology.
[34] Willy Govaerts,et al. MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs , 2003, TOMS.
[35] W. Schaffer,et al. Chaos reduces species extinction by amplifying local population noise , 1993, Nature.
[36] Yanni Xiao,et al. The dynamics of an eco-epidemic model with biological control , 2003 .
[37] Ezio Venturino,et al. Epidemics in predator-prey models: disease in the predators. , 2002, IMA journal of mathematics applied in medicine and biology.
[38] Mick G. Roberts,et al. The Dynamics of Bovine Tuberculosis in Possum Populations, and its Eradication or Control by Culling or Vaccination , 1996 .
[39] Vikas Rai,et al. Wave of Chaos and Pattern Formation in Spatial Predator-Prey Systems with Holling Type IV Predator Response , 2008 .
[40] Y. Iwasa,et al. Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models , 1986, Journal of mathematical biology.
[41] Thilo Gross,et al. Generalized models as a universal approach to the analysis of nonlinear dynamical systems. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.
[42] B W Kooi,et al. Stabilization due to predator interference: comparison of different analysis approaches. , 2008, Mathematical biosciences and engineering : MBE.
[43] Mark A. McPeek,et al. Chaotic Population Dynamics Favors the Evolution of Dispersal , 1996, The American Naturalist.
[44] G. Serio,et al. A generalization of the Kermack-McKendrick deterministic epidemic model☆ , 1978 .
[45] Alberto d’Onofrio,et al. Bifurcation Thresholds in an SIR Model with Information-Dependent Vaccination , 2007 .
[46] Stephen P. Ellner,et al. Living on the edge of chaos: population dynamics of fennoscandian voles , 2000 .
[47] E. Ranta,et al. Synchronous dynamics and rates of extinction in spatially structured populations , 1997, Proceedings of the Royal Society of London. Series B: Biological Sciences.
[48] H. McCallum,et al. How should pathogen transmission be modelled? , 2001, Trends in ecology & evolution.
[49] John Brindley,et al. Ocean plankton populations as excitable media , 1994 .
[50] Thilo Gross. Population dynamics: general results from local analysis , 2004 .
[51] O. Diekmann,et al. Patterns in the effects of infectious diseases on population growth , 1991, Journal of mathematical biology.
[52] T. O. Carroll,et al. Modeling the role of viral disease in recurrent phytoplankton blooms , 1994 .
[53] Y. Kuznetsov. Elements of Applied Bifurcation Theory , 2023, Applied Mathematical Sciences.
[54] N. Barlow,et al. Non‐linear transmission and simple models for bovine tuberculosis , 2000 .
[55] E. Venturino. The effects of diseases on competing species. , 2001, Mathematical biosciences.
[56] Thilo Gross,et al. Long food chains are in general chaotic , 2005 .
[57] J. Beddington,et al. Mutual Interference Between Parasites or Predators and its Effect on Searching Efficiency , 1975 .
[58] A. Dobson,et al. The Population Biology of Parasite-Induced Changes in Host Behavior , 1988, The Quarterly Review of Biology.
[59] Thilo Gross,et al. Computation and Visualization of bifurcation Surfaces , 2008, Int. J. Bifurc. Chaos.
[60] C. S. Holling. Some Characteristics of Simple Types of Predation and Parasitism , 1959, The Canadian Entomologist.
[61] Thilo Gross,et al. Instabilities in spatially extended predator-prey systems: spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations. , 2007, Journal of theoretical biology.