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Resilience of dynamical systems – ERRATUM
- Hana Krakovská, Christian Kuehn, Iacopo P. Longo
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- Journal:
- European Journal of Applied Mathematics / Volume 35 / Issue 1 / February 2024
- Published online by Cambridge University Press:
- 06 July 2023, p. 201
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Resilience of dynamical systems
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- Hana Krakovská, Christian Kuehn, Iacopo P. Longo
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- Journal:
- European Journal of Applied Mathematics / Volume 35 / Issue 1 / February 2024
- Published online by Cambridge University Press:
- 05 June 2023, pp. 155-200
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Stability is among the most important concepts in dynamical systems. Local stability is well-studied, whereas determining the ‘global stability’ of a nonlinear system is very challenging. Over the last few decades, many different ideas have been developed to address this issue, primarily driven by concrete applications. In particular, several disciplines suggested a web of concepts under the headline ‘resilience’. Unfortunately, there are many different variants and explanations of resilience, and often, the definitions are left relatively vague, sometimes even deliberately. Yet, to allow for a structural development of a mathematical theory of resilience that can be used across different areas, one has to ensure precise starting definitions and provide a mathematical comparison of different resilience measures. In this work, we provide a systematic review of the most relevant indicators of resilience in the context of continuous dynamical systems, grouped according to their mathematical features. The indicators are also generalised to be applicable to any attractor. These steps are important to ensure a more reliable, quantitatively comparable and reproducible study of resilience in dynamical systems. Furthermore, we also develop a new concept of resilience against certain nonautonomous perturbations to demonstrate how one can naturally extend our framework. All the indicators are finally compared via the analysis of a classic scalar model from population dynamics to show that direct quantitative application-based comparisons are an immediate consequence of a detailed mathematical analysis.
Towards sample path estimates for fast–slow stochastic partial differential equations
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- MANUEL V. GNANN, CHRISTIAN KUEHN, ANNE PEIN
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- Journal:
- European Journal of Applied Mathematics / Volume 30 / Issue 5 / October 2019
- Published online by Cambridge University Press:
- 28 September 2018, pp. 1004-1024
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Estimates for sample paths of fast–slow stochastic ordinary differential equations have become a key mathematical tool relevant for theory and applications. In particular, there have been breakthroughs by Berglund and Gentz to prove sharp exponential error estimates. In this paper, we take the first steps in order to generalise this theory to fast–slow stochastic partial differential equations. In a simplified setting with a natural decomposition into low- and high-frequency modes, we demonstrate that for a short-time period the probability for the corresponding sample path to leave a neighbourhood around the stable slow manifold of the system is exponentially small as well.
Scaling laws and warning signs for bifurcations of SPDEs
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- CHRISTIAN KUEHN, FRANCESCO ROMANO
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- European Journal of Applied Mathematics / Volume 30 / Issue 5 / October 2019
- Published online by Cambridge University Press:
- 18 September 2018, pp. 853-868
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Critical transitions (or tipping points) are drastic sudden changes observed in many dynamical systems. Large classes of critical transitions are associated with systems, which drift slowly towards a bifurcation point. In the context of stochastic ordinary differential equations, there are results on growth of variance and autocorrelation before a transition, which can be used as possible warning signs in applications. A similar theory has recently been developed in the simplest setting for stochastic partial differential equations (SPDEs) for self-adjoint operators in the drift term. This setting leads to real discrete spectrum and growth of the covariance operator via a certain scaling law. In this paper, we develop this theory substantially further. We cover the cases of complex eigenvalues, degenerate eigenvalues as well as continuous spectrum. This provides a fairly comprehensive theory for most practical applications of warning signs for SPDE bifurcations.
The Taipan Galaxy Survey: Scientific Goals and Observing Strategy
- Elisabete da Cunha, Andrew M. Hopkins, Matthew Colless, Edward N. Taylor, Chris Blake, Cullan Howlett, Christina Magoulas, John R. Lucey, Claudia Lagos, Kyler Kuehn, Yjan Gordon, Dilyar Barat, Fuyan Bian, Christian Wolf, Michael J. Cowley, Marc White, Ixandra Achitouv, Maciej Bilicki, Joss Bland-Hawthorn, Krzysztof Bolejko, Michael J. I. Brown, Rebecca Brown, Julia Bryant, Scott Croom, Tamara M. Davis, Simon P. Driver, Miroslav D. Filipovic, Samuel R. Hinton, Melanie Johnston-Hollitt, D. Heath Jones, Bärbel Koribalski, Dane Kleiner, Jon Lawrence, Nuria Lorente, Jeremy Mould, Matt S. Owers, Kevin Pimbblet, C. G. Tinney, Nicholas F. H. Tothill, Fred Watson
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- Journal:
- Publications of the Astronomical Society of Australia / Volume 34 / 2017
- Published online by Cambridge University Press:
- 24 October 2017, e047
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The Taipan galaxy survey (hereafter simply ‘Taipan’) is a multi-object spectroscopic survey starting in 2017 that will cover 2π steradians over the southern sky (δ ≲ 10°, |b| ≳ 10°), and obtain optical spectra for about two million galaxies out to z < 0.4. Taipan will use the newly refurbished 1.2-m UK Schmidt Telescope at Siding Spring Observatory with the new TAIPAN instrument, which includes an innovative ‘Starbugs’ positioning system capable of rapidly and simultaneously deploying up to 150 spectroscopic fibres (and up to 300 with a proposed upgrade) over the 6° diameter focal plane, and a purpose-built spectrograph operating in the range from 370 to 870 nm with resolving power R ≳ 2000. The main scientific goals of Taipan are (i) to measure the distance scale of the Universe (primarily governed by the local expansion rate, H0) to 1% precision, and the growth rate of structure to 5%; (ii) to make the most extensive map yet constructed of the total mass distribution and motions in the local Universe, using peculiar velocities based on improved Fundamental Plane distances, which will enable sensitive tests of gravitational physics; and (iii) to deliver a legacy sample of low-redshift galaxies as a unique laboratory for studying galaxy evolution as a function of dark matter halo and stellar mass and environment. The final survey, which will be completed within 5 yrs, will consist of a complete magnitude-limited sample (i ⩽ 17) of about 1.2 × 106 galaxies supplemented by an extension to higher redshifts and fainter magnitudes (i ⩽ 18.1) of a luminous red galaxy sample of about 0.8 × 106 galaxies. Observations and data processing will be carried out remotely and in a fully automated way, using a purpose-built automated ‘virtual observer’ software and an automated data reduction pipeline. The Taipan survey is deliberately designed to maximise its legacy value by complementing and enhancing current and planned surveys of the southern sky at wavelengths from the optical to the radio; it will become the primary redshift and optical spectroscopic reference catalogue for the local extragalactic Universe in the southern sky for the coming decade.
A meeting point of entropy and bifurcations in cross-diffusion herding†
- ANSGAR JÜNGEL, CHRISTIAN KUEHN, LARA TRUSSARDI
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- Journal:
- European Journal of Applied Mathematics / Volume 28 / Issue 2 / April 2017
- Published online by Cambridge University Press:
- 15 August 2016, pp. 317-356
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A cross-diffusion system modelling the information herding of individuals is analysed in a bounded domain with no-flux boundary conditions. The variables are the species' density and an influence function which modifies the information state of the individuals. The cross-diffusion term may stabilize or destabilize the system. Furthermore, it allows for a formal gradient-flow or entropy structure. Exploiting this structure, the global-in-time existence of weak solutions and the exponential decay to the constant steady state is proved in certain parameter regimes. This approach does not extend to all parameters. We investigate local bifurcations from homogeneous steady states analytically to determine whether this defines the validity boundary. This analysis shows that generically there is a gap in the parameter regime between the entropy approach validity and the first local bifurcation. Next, we use numerical continuation methods to track the bifurcating non-homogeneous steady states globally and to determine non-trivial stationary solutions related to herding behaviour. In summary, we find that the main boundaries in the parameter regime are given by the first local bifurcation point, the degeneracy of the diffusion matrix and a certain entropy decay validity condition. We study several parameter limits analytically as well as numerically, with a focus on the role of changing a linear damping parameter as well as a parameter controlling the cross-diffusion. We suggest that our paradigm of comparing bifurcation-generated obstructions to the parameter validity of global-functional methods could also be of relevance for many other models beyond the one studied here.
Contributors
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- By Mitchell Aboulafia, Frederick Adams, Marilyn McCord Adams, Robert M. Adams, Laird Addis, James W. Allard, David Allison, William P. Alston, Karl Ameriks, C. Anthony Anderson, David Leech Anderson, Lanier Anderson, Roger Ariew, David Armstrong, Denis G. Arnold, E. J. Ashworth, Margaret Atherton, Robin Attfield, Bruce Aune, Edward Wilson Averill, Jody Azzouni, Kent Bach, Andrew Bailey, Lynne Rudder Baker, Thomas R. Baldwin, Jon Barwise, George Bealer, William Bechtel, Lawrence C. Becker, Mark A. Bedau, Ernst Behler, José A. Benardete, Ermanno Bencivenga, Jan Berg, Michael Bergmann, Robert L. Bernasconi, Sven Bernecker, Bernard Berofsky, Rod Bertolet, Charles J. Beyer, Christian Beyer, Joseph Bien, Joseph Bien, Peg Birmingham, Ivan Boh, James Bohman, Daniel Bonevac, Laurence BonJour, William J. Bouwsma, Raymond D. Bradley, Myles Brand, Richard B. Brandt, Michael E. Bratman, Stephen E. Braude, Daniel Breazeale, Angela Breitenbach, Jason Bridges, David O. Brink, Gordon G. Brittan, Justin Broackes, Dan W. Brock, Aaron Bronfman, Jeffrey E. Brower, Bartosz Brozek, Anthony Brueckner, Jeffrey Bub, Lara Buchak, Otavio Bueno, Ann E. Bumpus, Robert W. Burch, John Burgess, Arthur W. Burks, Panayot Butchvarov, Robert E. Butts, Marina Bykova, Patrick Byrne, David Carr, Noël Carroll, Edward S. Casey, Victor Caston, Victor Caston, Albert Casullo, Robert L. Causey, Alan K. L. Chan, Ruth Chang, Deen K. Chatterjee, Andrew Chignell, Roderick M. Chisholm, Kelly J. Clark, E. J. Coffman, Robin Collins, Brian P. Copenhaver, John Corcoran, John Cottingham, Roger Crisp, Frederick J. Crosson, Antonio S. Cua, Phillip D. Cummins, Martin Curd, Adam Cureton, Andrew Cutrofello, Stephen Darwall, Paul Sheldon Davies, Wayne A. Davis, Timothy Joseph Day, Claudio de Almeida, Mario De Caro, Mario De Caro, John Deigh, C. F. Delaney, Daniel C. Dennett, Michael R. DePaul, Michael Detlefsen, Daniel Trent Devereux, Philip E. Devine, John M. Dillon, Martin C. Dillon, Robert DiSalle, Mary Domski, Alan Donagan, Paul Draper, Fred Dretske, Mircea Dumitru, Wilhelm Dupré, Gerald Dworkin, John Earman, Ellery Eells, Catherine Z. Elgin, Berent Enç, Ronald P. Endicott, Edward Erwin, John Etchemendy, C. Stephen Evans, Susan L. Feagin, Solomon Feferman, Richard Feldman, Arthur Fine, Maurice A. Finocchiaro, William FitzPatrick, Richard E. Flathman, Gvozden Flego, Richard Foley, Graeme Forbes, Rainer Forst, Malcolm R. Forster, Daniel Fouke, Patrick Francken, Samuel Freeman, Elizabeth Fricker, Miranda Fricker, Michael Friedman, Michael Fuerstein, Richard A. Fumerton, Alan Gabbey, Pieranna Garavaso, Daniel Garber, Jorge L. A. Garcia, Robert K. Garcia, Don Garrett, Philip Gasper, Gerald Gaus, Berys Gaut, Bernard Gert, Roger F. Gibson, Cody Gilmore, Carl Ginet, Alan H. Goldman, Alvin I. Goldman, Alfonso Gömez-Lobo, Lenn E. Goodman, Robert M. Gordon, Stefan Gosepath, Jorge J. E. Gracia, Daniel W. Graham, George A. Graham, Peter J. Graham, Richard E. Grandy, I. Grattan-Guinness, John Greco, Philip T. Grier, Nicholas Griffin, Nicholas Griffin, David A. Griffiths, Paul J. Griffiths, Stephen R. Grimm, Charles L. Griswold, Charles B. Guignon, Pete A. Y. Gunter, Dimitri Gutas, Gary Gutting, Paul Guyer, Kwame Gyekye, Oscar A. Haac, Raul Hakli, Raul Hakli, Michael Hallett, Edward C. Halper, Jean Hampton, R. James Hankinson, K. R. Hanley, Russell Hardin, Robert M. Harnish, William Harper, David Harrah, Kevin Hart, Ali Hasan, William Hasker, John Haugeland, Roger Hausheer, William Heald, Peter Heath, Richard Heck, John F. Heil, Vincent F. Hendricks, Stephen Hetherington, Francis Heylighen, Kathleen Marie Higgins, Risto Hilpinen, Harold T. Hodes, Joshua Hoffman, Alan Holland, Robert L. Holmes, Richard Holton, Brad W. Hooker, Terence E. Horgan, Tamara Horowitz, Paul Horwich, Vittorio Hösle, Paul Hoβfeld, Daniel Howard-Snyder, Frances Howard-Snyder, Anne Hudson, Deal W. Hudson, Carl A. Huffman, David L. Hull, Patricia Huntington, Thomas Hurka, Paul Hurley, Rosalind Hursthouse, Guillermo Hurtado, Ronald E. Hustwit, Sarah Hutton, Jonathan Jenkins Ichikawa, Harry A. Ide, David Ingram, Philip J. Ivanhoe, Alfred L. Ivry, Frank Jackson, Dale Jacquette, Joseph Jedwab, Richard Jeffrey, David Alan Johnson, Edward Johnson, Mark D. Jordan, Richard Joyce, Hwa Yol Jung, Robert Hillary Kane, Tomis Kapitan, Jacquelyn Ann K. Kegley, James A. Keller, Ralph Kennedy, Sergei Khoruzhii, Jaegwon Kim, Yersu Kim, Nathan L. King, Patricia Kitcher, Peter D. Klein, E. D. Klemke, Virginia Klenk, George L. Kline, Christian Klotz, Simo Knuuttila, Joseph J. Kockelmans, Konstantin Kolenda, Sebastian Tomasz Kołodziejczyk, Isaac Kramnick, Richard Kraut, Fred Kroon, Manfred Kuehn, Steven T. Kuhn, Henry E. Kyburg, John Lachs, Jennifer Lackey, Stephen E. Lahey, Andrea Lavazza, Thomas H. Leahey, Joo Heung Lee, Keith Lehrer, Dorothy Leland, Noah M. Lemos, Ernest LePore, Sarah-Jane Leslie, Isaac Levi, Andrew Levine, Alan E. Lewis, Daniel E. Little, Shu-hsien Liu, Shu-hsien Liu, Alan K. L. Chan, Brian Loar, Lawrence B. Lombard, John Longeway, Dominic McIver Lopes, Michael J. Loux, E. J. Lowe, Steven Luper, Eugene C. Luschei, William G. Lycan, David Lyons, David Macarthur, Danielle Macbeth, Scott MacDonald, Jacob L. Mackey, Louis H. Mackey, Penelope Mackie, Edward H. Madden, Penelope Maddy, G. B. Madison, Bernd Magnus, Pekka Mäkelä, Rudolf A. Makkreel, David Manley, William E. Mann (W.E.M.), Vladimir Marchenkov, Peter Markie, Jean-Pierre Marquis, Ausonio Marras, Mike W. Martin, A. P. Martinich, William L. McBride, David McCabe, Storrs McCall, Hugh J. McCann, Robert N. McCauley, John J. McDermott, Sarah McGrath, Ralph McInerny, Daniel J. McKaughan, Thomas McKay, Michael McKinsey, Brian P. McLaughlin, Ernan McMullin, Anthonie Meijers, Jack W. Meiland, William Jason Melanson, Alfred R. Mele, Joseph R. Mendola, Christopher Menzel, Michael J. Meyer, Christian B. Miller, David W. Miller, Peter Millican, Robert N. Minor, Phillip Mitsis, James A. Montmarquet, Michael S. Moore, Tim Moore, Benjamin Morison, Donald R. Morrison, Stephen J. Morse, Paul K. Moser, Alexander P. D. Mourelatos, Ian Mueller, James Bernard Murphy, Mark C. Murphy, Steven Nadler, Jan Narveson, Alan Nelson, Jerome Neu, Samuel Newlands, Kai Nielsen, Ilkka Niiniluoto, Carlos G. Noreña, Calvin G. Normore, David Fate Norton, Nikolaj Nottelmann, Donald Nute, David S. Oderberg, Steve Odin, Michael O’Rourke, Willard G. Oxtoby, Heinz Paetzold, George S. Pappas, Anthony J. Parel, Lydia Patton, R. P. Peerenboom, Francis Jeffry Pelletier, Adriaan T. Peperzak, Derk Pereboom, Jaroslav Peregrin, Glen Pettigrove, Philip Pettit, Edmund L. Pincoffs, Andrew Pinsent, Robert B. Pippin, Alvin Plantinga, Louis P. Pojman, Richard H. Popkin, John F. Post, Carl J. Posy, William J. Prior, Richard Purtill, Michael Quante, Philip L. Quinn, Philip L. Quinn, Elizabeth S. Radcliffe, Diana Raffman, Gerard Raulet, Stephen L. Read, Andrews Reath, Andrew Reisner, Nicholas Rescher, Henry S. Richardson, Robert C. Richardson, Thomas Ricketts, Wayne D. Riggs, Mark Roberts, Robert C. Roberts, Luke Robinson, Alexander Rosenberg, Gary Rosenkranz, Bernice Glatzer Rosenthal, Adina L. Roskies, William L. Rowe, T. M. Rudavsky, Michael Ruse, Bruce Russell, Lilly-Marlene Russow, Dan Ryder, R. M. Sainsbury, Joseph Salerno, Nathan Salmon, Wesley C. Salmon, Constantine Sandis, David H. Sanford, Marco Santambrogio, David Sapire, Ruth A. Saunders, Geoffrey Sayre-McCord, Charles Sayward, James P. Scanlan, Richard Schacht, Tamar Schapiro, Frederick F. Schmitt, Jerome B. Schneewind, Calvin O. Schrag, Alan D. Schrift, George F. Schumm, Jean-Loup Seban, David N. Sedley, Kenneth Seeskin, Krister Segerberg, Charlene Haddock Seigfried, Dennis M. Senchuk, James F. Sennett, William Lad Sessions, Stewart Shapiro, Tommie Shelby, Donald W. Sherburne, Christopher Shields, Roger A. Shiner, Sydney Shoemaker, Robert K. Shope, Kwong-loi Shun, Wilfried Sieg, A. John Simmons, Robert L. Simon, Marcus G. Singer, Georgette Sinkler, Walter Sinnott-Armstrong, Matti T. Sintonen, Lawrence Sklar, Brian Skyrms, Robert C. Sleigh, Michael Anthony Slote, Hans Sluga, Barry Smith, Michael Smith, Robin Smith, Robert Sokolowski, Robert C. Solomon, Marta Soniewicka, Philip Soper, Ernest Sosa, Nicholas Southwood, Paul Vincent Spade, T. L. S. Sprigge, Eric O. Springsted, George J. Stack, Rebecca Stangl, Jason Stanley, Florian Steinberger, Sören Stenlund, Christopher Stephens, James P. Sterba, Josef Stern, Matthias Steup, M. A. Stewart, Leopold Stubenberg, Edith Dudley Sulla, Frederick Suppe, Jere Paul Surber, David George Sussman, Sigrún Svavarsdóttir, Zeno G. Swijtink, Richard Swinburne, Charles C. Taliaferro, Robert B. Talisse, John Tasioulas, Paul Teller, Larry S. Temkin, Mark Textor, H. S. Thayer, Peter Thielke, Alan Thomas, Amie L. Thomasson, Katherine Thomson-Jones, Joshua C. Thurow, Vzalerie Tiberius, Terrence N. Tice, Paul Tidman, Mark C. Timmons, William Tolhurst, James E. Tomberlin, Rosemarie Tong, Lawrence Torcello, Kelly Trogdon, J. D. Trout, Robert E. Tully, Raimo Tuomela, John Turri, Martin M. Tweedale, Thomas Uebel, Jennifer Uleman, James Van Cleve, Harry van der Linden, Peter van Inwagen, Bryan W. Van Norden, René van Woudenberg, Donald Phillip Verene, Samantha Vice, Thomas Vinci, Donald Wayne Viney, Barbara Von Eckardt, Peter B. M. Vranas, Steven J. Wagner, William J. Wainwright, Paul E. Walker, Robert E. Wall, Craig Walton, Douglas Walton, Eric Watkins, Richard A. Watson, Michael V. Wedin, Rudolph H. Weingartner, Paul Weirich, Paul J. Weithman, Carl Wellman, Howard Wettstein, Samuel C. Wheeler, Stephen A. White, Jennifer Whiting, Edward R. Wierenga, Michael Williams, Fred Wilson, W. Kent Wilson, Kenneth P. Winkler, John F. Wippel, Jan Woleński, Allan B. Wolter, Nicholas P. Wolterstorff, Rega Wood, W. Jay Wood, Paul Woodruff, Alison Wylie, Gideon Yaffe, Takashi Yagisawa, Yutaka Yamamoto, Keith E. Yandell, Xiaomei Yang, Dean Zimmerman, Günter Zoller, Catherine Zuckert, Michael Zuckert, Jack A. Zupko (J.A.Z.)
- Edited by Robert Audi, University of Notre Dame, Indiana
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- The Cambridge Dictionary of Philosophy
- Published online:
- 05 August 2015
- Print publication:
- 27 April 2015, pp ix-xxx
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Distinctive histopathology and modulation of cytokine production during oral and intraperitoneal Trypanosoma cruzi Y strain infection
- CHRISTIAN C. KUEHN, LUIZ GUSTAVO R. OLIVEIRA, MARIZA ABREU MIRANDA, JOSÉ CLÓVIS PRADO, Jr.
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- Parasitology / Volume 141 / Issue 7 / June 2014
- Published online by Cambridge University Press:
- 19 February 2014, pp. 904-913
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Acute Chagas disease outbreaks are related to the consumption of food or drink contaminated by triatomine feces, thus making oral infection an important route of transmission. Both vector-borne and oral infections trigger important cardiac manifestations in the host that are related to a dysregulated immune response. The aims of this work were to evaluate possible alterations of lymphocyte CD4+/CD8+ sub-populations, Th1 and Th2 cytokines, nitrite concentrations and cardiac histopathology. One group of male Wistar rats was intraperitoneally infected (I.P.) with 1×105 metacyclic trypomastigotes of the T. cruzi Y strain, and another group of Wistar rats was orally infected (O.I.) with 8×105 metacyclic trypomastigotes of the same strain. The intraperitoneal infection triggered statistically enhanced parasite and peritoneal macrophage numbers, increased concentrations of NO and IL-12 and elevated cardiac inflammatory foci when compared with the oral infection. However, proliferation of CD4+ and CD8+ T cells were not statistically different for oral and intraperitoneal routes.