%0 Journal Article %1 Wang20122243 %A Wang, H. %A Castillo-Chavez, C. %D 2012 %J Discrete and Continuous Dynamical Systems - Series B %K imported %N 6 %P 2243-2266 %R http://dx.doi.org/10.3934/dcdsb.2012.17.2243 %T Spreading speeds and traveling waves for non-cooperative integro-difference systems %U http://dx.doi.org/10.3934/dcdsb.2012.17.2243 %V 17 %X The study of spatially explicit integro-difference systems when the local population dynamics are given in terms of discrete-time generations models has gained considerable attention over the past two decades. These nonlinear systems arise naturally in the study of the spatial dispersal of organisms. The brunt of the mathematical research on these systems, particularly, when dealing with cooperative systems, has focused on the study of the existence of traveling wave solutions and the characterization of their spreading speed. Here, we characterize the minimum propagation (spreading) speed, via the convergence of initial data to wave solutions, for a large class of non cooperative nonlinear systems of integro-difference equations. The spreading speed turns out to be the slowest speed from a family of non-constant traveling wave solutions. The applicability of these theoretical results is illustrated through the explicit study of an integro-difference system with local population dynamics governed by Hassell and Comins' non-cooperative competition model (1976). The corresponding integro-difference nonlinear systems that results from the redistribution of individuals via a dispersal kernel is shown to satisfy conditions that guarantee the existence of minimum speeds and traveling waves. This pa- per is dedicated to Avner Friedman as we celebrate his immense contributions to the fields of partial differential equations, integral equations, mathematical biology, industrial mathematics and applied mathematics in general. His leadership in the mathematical sciences and his mentorship of students and friends over several decades has made a huge difference in the personal and professional lives of many, including both of us.

@article{Wang20122243, abstract = {The study of spatially explicit integro-difference systems when the local population dynamics are given in terms of discrete-time generations models has gained considerable attention over the past two decades. These nonlinear systems arise naturally in the study of the spatial dispersal of organisms. The brunt of the mathematical research on these systems, particularly, when dealing with cooperative systems, has focused on the study of the existence of traveling wave solutions and the characterization of their spreading speed. Here, we characterize the minimum propagation (spreading) speed, via the convergence of initial data to wave solutions, for a large class of non cooperative nonlinear systems of integro-difference equations. The spreading speed turns out to be the slowest speed from a family of non-constant traveling wave solutions. The applicability of these theoretical results is illustrated through the explicit study of an integro-difference system with local population dynamics governed by Hassell and Comins' non-cooperative competition model (1976). The corresponding integro-difference nonlinear systems that results from the redistribution of individuals via a dispersal kernel is shown to satisfy conditions that guarantee the existence of minimum speeds and traveling waves. This pa- per is dedicated to Avner Friedman as we celebrate his immense contributions to the fields of partial differential equations, integral equations, mathematical biology, industrial mathematics and applied mathematics in general. His leadership in the mathematical sciences and his mentorship of students and friends over several decades has made a huge difference in the personal and professional lives of many, including both of us.}, added-at = {2017-11-10T22:48:29.000+0100}, affiliation = {Division of Mathematical and Natural Sciences, Arizona State University, Phoenix, AZ 85069, United States; Computational and Modeling Sciences Center, Arizona State University, PO Box 871904, Mathematics, Tempe, AZ 85287, United States; School of Human Evolution and Social Change, Arizona State University, Tempe, AZ 85282, United States; Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, United States; Biological Statistics and Computational Biology, Cornell University, Ithaca, NY 14853 - 2601, United States}, author = {Wang, H. and Castillo-Chavez, C.}, author_keywords = {Biological invasion; Dispersal; Integro- difference systems; Minimum speed; Traveling wave}, biburl = {https://www.bibsonomy.org/bibtex/2faf9944a6a438defb3bf74d3168a4d90/ccchavez}, correspondence_address1 = {Wang, H.; Division of Mathematical and Natural Sciences, Arizona State University, Phoenix, AZ 85069, United States; email: haiyan.wang@asu.edu}, date-added = {2017-11-10 21:45:26 +0000}, date-modified = {2017-11-10 21:45:26 +0000}, document_type = {Article}, doi = {http://dx.doi.org/10.3934/dcdsb.2012.17.2243}, interhash = {7068b6035935f707ba630c787ae2f963}, intrahash = {faf9944a6a438defb3bf74d3168a4d90}, issn = {15313492}, journal = {Discrete and Continuous Dynamical Systems - Series B}, keywords = {imported}, language = {English}, number = 6, pages = {2243-2266}, timestamp = {2017-11-10T22:48:29.000+0100}, title = {Spreading speeds and traveling waves for non-cooperative integro-difference systems}, url = {http://dx.doi.org/10.3934/dcdsb.2012.17.2243}, volume = 17, year = 2012 }