Cushing, Jim. M. - Department of Mathematics, University of Arizona

• DownloadedBy:[UniversityofArizona]At:18:5820April2007 Journal of Biological Dynamics
• On Preserving Stability of Volterra Integral Equations under a General Class of Perturbations
• Socially induced Synchronization of every-other-day egg laying in a Seabird colony
• PLEASE SCROLL DOWN FOR ARTICLE This article was downloaded by: [Cushing, Jim M]
• PLEASE SCROLL DOWN FOR ARTICLE This article was downloaded by: [Cushing, Jim M]
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• Using stage-structured evolutionary game theory to model the experimentally observed evolution
• Three Stage Semelparous Leslie Models J. M. Cushing
• Evolution of Corn Oil Sensitivity in the Flour Beetle Program in Applied Mathematics
• Journal of Biological Dynamics Vol. 1, No. 1, January 2007, 95107
• Nonlinearity and Stochasticity in Population J. M. Cushing
• Some Discrete Competition Models and the Principle of Competitive Exclusion
• Dynamics of hierarchical models in discrete-time
• Anatomy of a chaotic attractor: Subtle model-predicted patterns revealed in population data
• Received 31 January 2003 Accepted 10 April 2003
• Cycle Chains and the LPA J.M. CUSHING
• J. Math. Anal. Appl. 280 (2003) 102122 www.elsevier.com/locate/jmaa
• A Periodically Forced BevertonHolt J.M. CUSHINGa,
• OIKOS 98: 1724, 2002 Basins of attraction: population dynamics with two stable 4-cycles
• J. of Dierence Equations and Applications, 2002, Vol. 8(1), pp. 61 73 GeometricTransient Solutions
• Global Dynamics of Some Periodically Forced, Monotone Difference Equations
• This article was downloaded by:[University of Arizona] On: 9 November 2007
• Chiang, T. Olson, J. Dice, J. Biol. Chem. 267, 9202 (1992); H. Wiech, J. Buchner, M. Zimmermann, R.
• J. Math. Biol. (1991) 29:457-473 Mathematical
• J. Math. Biol. (1986) 24:381-403 Mathematical
• J. Math. Biology (1984) 20:259-276 ,Journal of
• J. Math. Biology 10, 385-400 (1980) 9Journal of Mathematical
• Aequationes Math. 13 (1975),89-96. University of Waterloo Birkhauser Verlag, Basel Extremal tests for scalar functions of several real variables at
• Strong Stability of Perturbed Systems of Volterra Integral Equations
• Applicable Analysis, 1975, Vol. 5, pp. 65-77 c'Gordon acd S r e ~ c k S ~ c l m c c?.;$!is!:crs it?
• JOURNAL OF DIFFERENTIAL EQUATIONS 20, 61-70 (1976) Bounded Solutions of Perturbed Volterra
• PLEASE SCROLL DOWN FOR ARTICLE This article was downloaded by: [Cushing, Jim M]
• Matrix Models and Population J. M. Cushing
• Predicting the dynamics of animal behaviour in field populations
• Journal of Mathematical Biology 3, 369--380 (1976) 9 by Springer-Verlag 1976
• DownloadedBy:[UniversityofArizona]At:17:388November2007 Journal of Biological Dynamics
• STUDENT SOLUTION MANUAL DIFFERENTIAL EQUATIONS
• SIAM J. APPLIED DYNAMICAL SYSTEMS c 2003 Society for Industrial and Applied Mathematics Vol. 2, No. 2, pp. 238253
• Advances in Ecological Research, Volume 37, 2005, 101-141 Nonlinear stochastic population dynamics
• Funkcialaj Ekvacioj, 20 (1977) 237-245 Strongly Admissible Operators and Banach Space
• Digital Object Identifier (DOI): 10.1007/s00285-006-0382-6
• Chaos and population control of insect outbreaks We used small perturbations in adult numbers to control large fluctuations in the
• MATHEMATICAL BIOSCIENCES http://www.mbejournal.org/ AND ENGINEERING
• Nonlinear Studies Nonlinear Studies Vol. 17, No. 1, pp. 1-13, 2010 I&S Publishers
• J. Math. Biology (1982) 14:231-250 Journal alr
• J. Math. Biol. (1987) 24:627-649 Journal olr
• Funkcialaj Ekvacioj, 15 (197?), 101-117 Some Stability Criteria for Linear
• A Simple Model of Cannibalism J. M. CUSHING
• Ecological Monographs, 71(2), 2001, pp. 277303 2001 by the Ecological Society of America
• J. Math. Biology (1985) 23:15-39 Mathematical
• * Supported, in part, by NSF grant DMS-9306271. J. Math. Biol. (1997) 36: 201--226
• Random Perturbations and Lattice Effects in Chaotic
• Funkcialaj Ekvacioj, 19 (1976) 79-84 Admissible Operators and Solutions of
• Some Discrete Competition Models and the Competitive Exclusion Principle
• Journal of Difference Equations and Applications, 1996 OPA (Overseas Publishers Association) 1996, Vol, 2, pp, 31-37 Amsterdam B,V Published in The Netherlands
• SIAM J. APPL. MATH. c 2006 Society for Industrial and Applied Mathematics Vol. 67, No. 1, pp. 2445
• DIFFERENTIAL EQUATIONS: AN APPLIED APPROACH
• ERRATA & NOTES 22 April 2008
• MATHEMATICAL BIOSCIENCES http://www.mbejournal.org/ AND ENGINEERING
• Competitive Outcomes Changed by Evolution R. C. Rael1
• On Strong Stability for Linear Integral Equations J. M. BOWNDS
• Bulletin of Mathematical Biology (2008) 70: 12721296 DOI 10.1007/s11538-008-9299-0
• J. Math Biology 6, 145-161 (1978) bySpringer-Verlag1978
• Funkcialaj Ekvacioj 19 (1976) 101-111 Existence, Uniqueness, and Extendibility of
• OIKOS 102: 329339, 2003 Can noise induce chaos?
• J. Math. Biology 4, 257--264 (1977) 9 by Springer-Verlag 1977
• 7. I. Aramori and S. Nakanishi, ibid. 8, 757 (1992). 8. CHO cells expressing mGluR1 or MEF cells trans-
• J. Math. Biol.(1994) 32:705-729 Mathematical
• SomeExistenceTheorems for NonlinearEigenvatueProblemsAssociated
• 17-Jan-06 To Appear in Ecological Letters Experimental support of the scaling rule for demographic
• Joitrnol of Ulflerence EqrrorC?nsand Applicorion3. 6: IYYh OPA (Overseas Publishers Association) 1996. Vol. 2. pp. 117-137 Amsterdam B.V. Puhlished in The Netherlands
• JOURNAL OF DIFFERENTIAL EQUATIONS 8, 512-522 (1970) Local Uniqueness for Harmonic Functions
• NATURAL RESOURCE MODELING Volume 8, Number 4, Fall 1994
• J. Math. Biol. (1996) 34: 755--772 Hierarchical models of intra-specific competition
• Lattice Effects Observed in Chaotic Dynamics of
• An Application: Antibiotic Control of an Infection The bacterium Staphylococcus aureus grows at a
• ( ) ( ) ( )General solution where x t ce P t p t dt
• MATH 129 Calculus II Section 16, Fall 2011
• FINAL EXAM REVIEW PACKET ANSWERS (Revised Fall 2011)
• IMPROPER INTEGRALS Does the infinite region beneath this curve
• BIFURCATION DIAGRAMS Plot equilibria x against the parameter p
• Definition of Definite Integral From Calc I : Page 265 in text
• Test 1 -Answers Math 129, Section 16 -13 September 2011
• 4.4 MATRIX NOTATION x t x t x t
• Sample Test 3 1. Use the Integral Test to determine if the following series converges or diverges
• If is a fundamental solution matrix of then the general solution of
• Chapter 5.4 Phase Plane Portraits for autonomous homogeneous systems
• Slope Fields ( , )x f t x
• CONVERGENCE & DIVERGENCE TESTS converges converges ( )
• Test 2 -Answers Math 129, Section 16 -13 October 2011
• ( ).Suppose is an equilibrium of THEOREM 1.4
• The general solution of a 2 dimensional linear homogeneous system is a 2 dimensional linear vector space.
• Case 1: two real and different eigenvalues Case 2: complex (conjugate) eigenvalues
• ( ) ( )converges converges g x dx f x dx
• Recall ... Note: In these examples of autonomous equations,
• FINAL EXAM REVIEW PACKET (Revised Fall 2011)
• JID:YJMAA AID:16253 /FLA [m3G; v 1.58; Prn:29/09/2011; 15:56] P.1 (1-10) J. Math. Anal. Appl. ()
• 1. Both Re 0 ( , ) is (locally) stable.i e ex y Linearization and stability
• Test 3 -Answers Math 129, Section 16
• ( ) converges ( ) converges g x dx f x dx
• where is a small parameter( , , )x f t x A solution ( ) is a function of
• Sample Test 2 1. Consider the integral
• x = amount of pesticide y = amount of pesticide y r x r r y
• This article was downloaded by: [University of Arizona], [J. M. Cushing] On: 07 November 2011, At: 16:14
• AN APPLICATION Exponential Growth
• ANSWERS TEST 1 ( Take-Home Portion -Due October 25 )
• CHAPTER 7: Nonlinear Systems Autonomous Systems
• Chapter 5.4 Phase Plane Portraits for autonomous homogeneous systems
• 1. 3D plot of (t, x, y) 2. Individual "time series" plots of x against t & y against t .
• Questions to address 1. Will this treatment work (i.e., eradicate the infection)?
• Chapter 3: Nonlinear First Order Equations Chapter 3.1: Autonomous Equations ( )x f x
• J. Math. Biol. (2009) 59:75104 DOI 10.1007/s00285-008-0208-9 Mathematical Biology
• h px x te x x xhasgeneralsolution q t te eList from
• ( ) ( )x f x x g x 1) the same number of equilibria
• hassolution on hassolution on .
• Step size s Approximation to x1 0.100000 5.862897
• Two most common procedures for drawing slope files are: Grid Method
• 0, 1, 1, 0.01r K c a The Spruce Budworm Model
• What is an ODE ? 1. From integral calculus: ( )
• BIFURCATION DIAGRAMS Plot equilibria x against the parameter p
• Chapter 3.4.2 Perturbation approximations ODE has a coefficent
• Chapter 3: Nonlinear Equations Chapter 3.1: Autonomous Equations
• P t P t P s x t x e e e q s ds
• Chapter 1-3: One ODE in one unknown 0 0( , ), ( )x f t x x t x
• increasesandis unbounded,if thereisnoequilibrium