{VERSION 1 0 "X11/Motif" "1.0"}{GLOBALS 3 1}{FONT 0 "-adobe-helve tica-bold-r-normal--*-140-*" "helvetica" "Helvetica-Bold" 8 14 0 "Helvetica-Bold" 12}{FONT 1 "-adobe-times-medium-r-normal--*-140- *" "times" "Times-Roman" 4 14 64 "Times-Roman" 12}{FONT 2 "-adobe -courier-medium-r-normal--*-140-*" "courier" "Courier" 4 14 192 " Courier" 12}{SCP_R 1 0 104{INP_R 2 0 "> "{TEXT 0 28 "with(linalg) :with (DEtools):"}}{OUT_R 3 0 2{TEXT 2 71 "Warning: new definitio n for norm\012Warning: new definition for trace\012"}}{COM_R 4 0{TEXT 1 151 "This is the maple work used in calculating the ei genvalues of the system and exploring other important aspects of \+ the differential system of equations."}}{INP_R 5 0 "> "{TEXT 0 0 ""}}{COM_R 6 0{TEXT 1 12 "c2=3 w=0.3 a"}}{INP_R 7 0 "> "{TEXT 0 136 "solve(\{y=0 ,-x-(c1 + 3*(x-y)^2)*y + 3*w=0 , lambda*z - 3/10 *w - 1*(z^2 + w^2)*z =0, 3/10*z + lambda*w -1*(z^2 + w^2)*w=0\} , \{x,y,z,w\} );"}}{OUT_R 8 0 7{DAG %2,5=3n3\`y`j2x0000=3n3\`z`p5= 3n3\`w`p5=3n3\`x`p5}}{INP_R 9 0 "> "{TEXT 0 0 ""}}{INP_R 10 0 "> \+ "{TEXT 0 125 "f:=vector([y,-x-(c1 + 3*(x-y)^2)*y + 3*w + 0*z , la mbda*z - 3/10*w - 1*(z^2 + w^2)*z , 3/10*z + lambda*w - 1*(z^2 + \+ w^2)*w]);"}}{OUT_R 11 0 10{DAG :3n3\`f`(3n4\`VECTOR`,2[2,5n3\`y`+ 7n3\`x`i2x0001*5+5n3\`c1`j2x0001*3+5pDp15pApFj2x0002j2x0003p15pAp 15pFn3\`w`p1F+7*5n4\`lambda`p15n3\`z`p15p15p25/3i2x0003j2x0010*5+ 5*3p2Ep1Dp15*3p25p1Dp15p15p2Ep15pF+7p2E/3p1Fp36*5p2Ap15p25p15p15* 5p39p15p25p15pF}}{INP_R 12 0 "> "{TEXT 0 26 "g:=jacobian(f, [x,y, z,w]);"}}{OUT_R 13 0 12{DAG :3n3\`g`(3n4\`MATRIX`,2[2,5[2,5j2x000 0j2x0001pCpC[2,5+5i2x0001pE*5+5n3\`x`j2x0006n3\`y`i2x0006pEp1EpEp 15+7*5+5p1Ap20p1Ep1CpEp1EpEp15n3\`c1`p15*3+5p1ApEp1Ep15j2x0002i2x 0003pCj2x0003[2,5pCpC+7n4\`lambda`pE*3n3\`z`p3Ap3C*3n3\`w`p3Ap15+ 5/3p3Cj2x0010pE*5p50pEp4BpEi2x0002[2,5pCpC+5/3p3Fp57pEp5Ap5F+7p46 pEp4Fp3Cp4Ap15}}{INP_R 14 0 "> "{TEXT 0 0 ""}}{INP_R 15 0 "> " {TEXT 0 38 "e:=((subs(x=0,y=0,z=0,w=0,evalm(g))));"}}{OUT_R 16 0 15{DAG :3n3\`e`(3n4\`MATRIX`,2[2,5[2,5j2x0000j2x0001pCpC[2,5i2x00 01+3n3\`c1`p14pCj2x0003[2,5pCpCn4\`lambda`/3i2x0003j2x0010[2,5pCp C/3p1Bp27p21}}{INP_R 17 0 "> "{TEXT 0 13 "eigenvals(e);"}}{OUT_R 18 0 17{DAG ,5+5n4\`lambda`j2x0001n3\`I`/3j2x0003j2x0010+5p2p5p7/ 3i2x0003pC+5n3\`c1`/3i2x0001j2x0002*3+5*3p17p1Cp5i2x0004p5/3p5p1C p27+5p17p19p1Ep19}}{COM_R 19 0{TEXT 1 237 "THESE ARE THE CONDITIO NS THAT DETERMINE THE STABILITY OF THE SYSTEM\015\015If lambda \+ > 0 and c1 > 0 then saddle at (0,0,0,0)\015If lambda > 0 and c 1 < 0 then source\015If lamdba < 0 and c1 > 0 then sink\015If \+ lambda < 0 and c1 < 0 then source"}}{INP_R 20 0 "> "{TEXT 0 1 " "}}{COM_R 21 0{TEXT 1 94 "The following is a representation of t he stability of the system with respect to c1 and lambda"}}{INP_R 22 0 "> "{TEXT 0 275 "PLOT(POLYGONS([ [2,2 ],[-2,2],[-2,-2],[2,- 2] ] , STYLE(LINE) ), TEXT( [1.0,1.0], 'SADDLE'), TEXT([-1,1], ' SOURCE'), \+ TEXT([-1,-1] , ' SOURCE' ), TEXT( [1,-1], 'SINK'), AXESLABEL S('C1','Lambda' ), 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00000000000000000000000000000000000000001030000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000001F0300000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000003000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000030000000000000000000000000000000000 0000000000000000000000000000}}{INP_R 25 0 "> "{TEXT 0 24 "factor( charpoly(e,x))=0;"}}{OUT_R 26 0 25{DAG =3+3*5+9*3n3\`x`j2x0002j2x 0100*5p5j2x0001n4\`lambda`pDi2x0200*3pFp7p9j2x0009pDpD+7p4pD*5p5p Dn3\`c1`pDpDpDpDpD/3pDp9j2x0000}}{INP_R 27 0 "> "{TEXT 0 0 ""}} {SEP_R 28 0}{COM_R 29 0{TEXT 1 182 "It the differential equations for z and w are seperable from the rest of the system because t hey do not depend on x or y.\015Thus it may be possible to solve \+ for a solution to z and w."}}{INP_R 30 0 "> "{TEXT 0 88 "f:=vecto r([ lambda*z - 3/10*w - 1*(z^2 + w^2)*z , 3/10*z + lambda*w - 1*( z^2 + w^2)*w]);"}}{OUT_R 31 0 30{DAG :3n3\`f`(3n4\`VECTOR`,2[2,3+ 7*5n4\`lambda`j2x0001n3\`z`pFpFn3\`w`/3i2x0003j2x0010*5+5*3p11j2x 0002pF*3p15p20pFpFp11pFi2x0001+7p11/3j2x0003p1A*5pCpFp15pFpF*5p1D pFp15pFp2A}}{INP_R 32 0 "> "{TEXT 0 22 "h:=jacobian(f, [z,w]);"}} {OUT_R 33 0 32{DAG :3n3\`h`(3n4\`MATRIX`,2[2,3[2,3+7n4\`lambda`j2 x0001*3n3\`z`j2x0002i2x0003*3n3\`w`p15i2x0001+5/3p17j2x0010p10*5p 1Ap10p13p10i2x0002[2,3+5/3j2x0003p22p10p25p2A+7pDp10p19p17p12p1D} }{INP_R 34 0 "> "{TEXT 0 27 "he:=subs(w=0,z=0,evalm(h));"}}{OUT_R 35 0 34{DAG :3n3\`he`(3n4\`MATRIX`,2[2,3[2,3n4\`lambda`/3i2x0003 j2x0010[2,3/3j2x0003p12pC}}{INP_R 36 0 "> "{TEXT 0 14 "eigenvals( he);"}}{OUT_R 37 0 36{DAG ,3+5n4\`lambda`j2x0001n3\`I`/3j2x0003j2 x0010+5p2p5p7/3i2x0003pC}}{SEP_R 38 0}{INP_R 39 0 "> "{TEXT 0 120 "dd:=(dsolve(\{diff(z(t),t)=lambda*z(t) - 3/10*w(t), diff(w(t),t )= 3/10*z(t) + lambda*w(t), w(0)=a,z(0)=b\}, \{z(t),w(t)\}));"}} {OUT_R 40 0 39{DAG :3n3\`dd`%2,3=3(3n3\`w`,2n3\`t`+5*7n3\`b`j2x00 01(3n3\`exp`,2*5pAp10n4\`lambda`p10p10(3n3\`sin`,2+3pA/3j2x0003j2 x0010p10p10*7n3\`a`p10p12p10(3n3\`cos`p21p10p10=3(3n3\`z`p9+5*7p2 Cp10p12p10p1Ep10i2x0001*7pEp10p12p10p31p10p10}}{COM_R 41 0{TEXT 1 187 "This is the linearization of z and w at the origin. Notice that if lambda is negative then the solution decays to the origi n whereas when lambda is positive the solutions go to infinity."} }{COM_R 42 0{TEXT 1 62 "\015\015The non-linearized solutions to z and w are calculated below"}}{INP_R 43 0 "> "{TEXT 0 141 "non:=s implify(dsolve(\{diff(z(t),t)=lambda*z - 3/10*w - ((z)^2 + (w)^2) *z , diff(w(t),t)= 3/10*z + lambda*w - ((z)^2 +(w)^2)*w\},\{z(t), w(t)\}));"}}{OUT_R 44 0 43{DAG :3n3\`non`%2,3=3(3n3\`w`,2n3\`t`+B n3\`_C1`j2x0001*5pApFn3\`z`pF/3j2x0003j2x0010*7pApFn4\`lambda`pFp 7pFpF*7pApFp7pFp14j2x0002i2x0001*5pApFp7p18p2E=3(3p14p9+Bn3\`_C2` pF*7pApFp1FpFp14pFpF*5pApFp7pF/3i2x0003p1A*5pApFp14p18p2E*7pApFp1 4pFp7p2Cp2E}}{COM_R 45 0{TEXT 1 165 "This is a solution, but it i s not very revealing of the behavior of the system. A more effec tive method is to solve the differential system using polar coord inates."}}{COM_R 46 0{TEXT 1 404 "\015The equations w an z can b e re-written in terms of r and theta : \015z= r cos (theta)\015w= r sin (theta)\015substituting these equations into the differenti al equations for w and z and solving for r' and theta' yeilds\015 r'= lambda*r -A* r^3\015\015 theta '= 3/10 or theta'=omega\0 15\015thus integrating theta' : theta= omega *t + fii \015"}}{INP_R 47 0 "> "{TEXT 0 22 "dr:= lambda*r - A*r^3 ;"}}{OUT_R 48 0 47{DAG :3n3\`dr`+5*5n4\`lambda`j2x0001n3\`r`p8p8* 5n3\`A`p8pAj2x0003i2x0001}}{INP_R 49 0 "> "{TEXT 0 21 "theta:=ome ga*t + phi;"}}{OUT_R 50 0 49{DAG :3n4\`theta`+5*5n4\`omega`j2x000 1n3\`t`p9p9n3\`phi`p9}}{INP_R 51 0 "> "{TEXT 0 33 "(dsolve(\{diff (r(t),t)=dr\},r(t)));"}}{OUT_R 52 0 51{DAG =3*3(3n3\`r`,2n3\`t`i2 x0002*5+5n3\`A`j2x0001*7(3n3\`exp`,2+3*5p6pEn4\`lambda`pEp8pEn3\` _C1`pEp19pEpEpEp19i2x0001}}{COM_R 53 0{TEXT 1 62 "If lambda > 0 \+ then as t -> infinity r -> sqrt (lambda) thus"}}{INP_R 54 0 "> \+ "{TEXT 0 29 "z:=sqrt(lambda/A)*cos(theta);"}}{OUT_R 55 0 54{DAG : 3n3\`z`*5*5n4\`lambda`j2x0001n3\`A`i2x0001/3p8j2x0002(3n3\`cos`,2 +5*5n4\`omega`p8n3\`t`p8p8n3\`phi`p8p8}}{COM_R 56 0{TEXT 1 3 "and "}}{INP_R 57 0 "> "{TEXT 0 29 "w:=sqrt(lambda/A)*sin(theta);"}} {OUT_R 58 0 57{DAG :3n3\`w`*5*5n4\`lambda`j2x0001n3\`A`i2x0001/3p 8j2x0002(3n3\`sin`,2+5*5n4\`omega`p8n3\`t`p8p8n3\`phi`p8p8}} {COM_R 59 0{TEXT 1 99 "This means that there is a circular lim it cycle in the z-w plane with a radii of sqrt(lambda/A)."}} {COM_R 60 0{TEXT 1 66 "Otherwise if lambda < 0 then as t-> infini ty z and w go to zero."}}{COM_R 61 0{TEXT 1 50 "\015\015Now it \+ is time to do some Bifurcation diagrams. "}}{INP_R 62 0 "> "{TEXT 0 13 "with (plots);"}}{OUT_R 63 0 62{DAG [2,22n4\`animate`n5\`an imate3d`n5\`conformal`n5\`contourplot`n6\`cylinderplot`n5\`densit yplot`n4\`display`n5\`display3d`n5\`fieldplot`n5\`fieldplot3d`n5\ `gradplot`n5\`gradplot3d`n6\`implicitplot`n6\`implicitplot3d`n5\` loglogplot`n4\`logplot`n5\`matrixplot`n4\`odeplot`n5\`pointplot`n 5\`polarplot`n5\`polygonplot`n6\`polygonplot3d`n6\`polyhedraplot` n4\`replot`n5\`setoptions`n6\`setoptions3d`n5\`spacecurve`n7\`spa rsematrixplot`n5\`sphereplot`n5\`surfdata`n5\`textplot`n5\`textpl ot3d`n5\`tubeplot`}}{COM_R 64 0{TEXT 1 1 "\015"}}{COM_R 65 0{TEXT 1 181 "First I will do a bifurcation diagram for the asymptotic \+ solution of r: \015r' is zero when r=0 and r= (+or-)sqrt(lambda /A). The point r=0 is unstable and the other point is stable."}} {INP_R 66 0 "> "{TEXT 0 54 "plot( \{sqrt(lambda),-sqrt(lambda) , \+ 0\}, lambda=0..5 );"}}{GRH_R 67 0{RASTER 500 401 1 63 00000000000 0FCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF03000000000000000000000000FEF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF070000000000000000000000000600000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000600000000000000000000000006000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000006000000000000000000000000060000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000060000000000000000000000000600000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000600000000000000000000000006000000000000000000000 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0000000000}}{COM_R 68 0{TEXT 1 88 "The top and bottom lines repre sent stable solutions while r=0 is the only unstable line."}} {COM_R 69 0{TEXT 1 101 "Since theta' is a constant theta' will n ever equal zero and thus does not have a bifurcation diagram"}} {COM_R 70 0{TEXT 1 247 "--------------------------------------\01 5\015If lambda is less than zero then the asymptotic solutions o f x and y are uncoupled from w and z since w and z go to zero as \+ t->infinity. Thus I shall attempt to solve for this special case of x and y. "}}{INP_R 71 0 "> "{TEXT 0 0 ""}}{INP_R 72 0 "> \+ "{TEXT 0 38 "v:=vector([y,-x-(c1 + 3*(x-y)^2)*y ]);"}}{OUT_R 73 0 72{DAG :3n3\`v`(3n4\`VECTOR`,2[2,3n3\`y`+5n3\`x`i2x0001*5+5n3\`c 1`j2x0001*3+5pDp15pApFj2x0002j2x0003p15pAp15pF}}{INP_R 74 0 "> " {TEXT 0 22 "j:=jacobian(v, [x,y]);"}}{OUT_R 75 0 74{DAG :3n3\`j`( 3n4\`MATRIX`,2[2,3[2,3j2x0000j2x0001[2,3+5i2x0001pE*5+5n3\`x`j2x0 006n3\`y`i2x0006pEp1CpEp13+7*5+5p18p1Ep1Cp1ApEp1CpEp13n3\`c1`p13* 3+5p18pEp1Cp13j2x0002i2x0003}}{INP_R 76 0 "> "{TEXT 0 0 ""}} {INP_R 77 0 "> "{TEXT 0 30 "e:=((subs(x=0,y=0,evalm(j))));"}} {OUT_R 78 0 77{DAG :3n3\`e`(3n4\`MATRIX`,2[2,3[2,3j2x0000j2x0001[ 2,3i2x0001+3n3\`c1`p12}}{INP_R 79 0 "> "{TEXT 0 13 "eigenvals(e); "}}{OUT_R 80 0 79{DAG ,3+5n3\`c1`/3i2x0001j2x0002*3+5*3p2p7j2x000 1i2x0004pE/3pEp7p13+5p2p4p9p4}}{INP_R 81 0 "> "{TEXT 0 0 ""}} {INP_R 82 0 "> "{TEXT 0 88 "dsolve(\{diff(x(t),t)=y(t) , diff(y(t ),t)=-x(t)-(c1 + 3*(x(t)-y(t) )^2)*y(t) \}, \{x(t)\} );"}}{COM_R 83 0{TEXT 1 280 "Maple cannot solve this differential equation. \+ Thus I am stuck with numerical methods for solutions and the usin g coordinate transforms has not revealed any simpler forms..\015- ------------------------\015\015\015I shall now do Bifurcation di agrams for x and y when lambda is less than zero "}}{COM_R 84 0 {TEXT 1 232 "\015the only fixed points of the x-y system are 0,0\ 015The equation x'=y does not have any constants that the fixed p oint can depend on. The only fixed point for this equation is y \+ = 0. There cannot be a Bifurcation diagram for x'=y. "}}{COM_R 85 0{TEXT 1 190 "The equation for y' , however, has the constan t c1 that can be varied to change the locations of where y'=0. N otice that the only place that both x' and y' can equal zero is a t the origin "}}{INP_R 86 0 "> "{TEXT 0 37 "solve(\{-x-(c1+3*(x - y)^2)*y=0\},\{c1\});"}}{OUT_R 87 0 86{DAG %2,2=3n3\`c1`*5+9n3\`x` i2x0001*5n3\`y`j2x0001p7j2x0002i2x0003*5p7pEpCp11j2x0006*3pCj2x00 03p13pEpCp9}}{INP_R 88 0 "> "{TEXT 0 121 "plot3d ( (-x-3*y*x^2 +6 *x*y^2 -3*y^3 )/y, x=-3..3, y=-3..3, labels=[x,y,C1] , title=( Rate_of_y_is_Zero_at_Surface) ); "}}{GRH_R 89 0{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00000000000000000000000000000000000000000000000000000000000000080 00000000000000000000000000000000000000F03900000000000000000000000 00000000000000000000000000000000000000000000000000000000000880000 00000000000000000000000000000000000040000000000000000000000000000 00000000000000000000000000000000000000000000000000000007000000000 00000000000000000000000000000000400000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000004400000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000038000000000000000000000000000000}}{COM_R 90 0{TEXT 1 1367 " This is a cool graph of the parabloid isosu rface where y'=0 when lambda < 0 and t->infinity_. It is a type of bifurcation diagram. Each point on the surface is a value of x, y, and c1 where y'=0. \015If c1 is greater than zero y is st able. In this graph c1 is negative, and thus the surface you see is where y is unstable. Along the line x=0 the value of c1 on \+ the y'=0 surface is -3y^2 which is always negative. At x =0 and y=0 c1 is zero and the stability of y' is undetermined. Along \+ the line y=0 there is only one point where c1 is defined and that is at x=0. Elsewhere c1 blows up to infinity. This dovetails wi th our observation that the only fixed point in the x-y plane is \+ at the origin. To further characterize this surface I attempted \+ solving for c1>0. However I was unsuccessfull. The surface is discontinuous at y=0 and c1 goes to +or-infinity. Considering a finite value for c1 it is obvious that y' can never equal zero a long the plane y=0 unless x=0. \015\015\015 What about if c1= \+ 0 and lambda < 0 ? Then the system of equations reduces to [x'= y, y'=-x ] or to single equations x''+x = 0 or y'' + y=0. Th ese have solutions of the form A*sin(t) + B*cos(t) which is pur ely periodic. There for if c1=0 and lambda<0 the trajectories \+ in the x, y plane will settle into periodic orbits as t grows lar ge and w and z will go to zero."}}{COM_R 91 0{TEXT 1 184 "\015\0 15What happens when lambda is larger than zero? Then the equatio ns for x' and y' become zero when x=0,y=0 and w=0 since we know t he asymptotic solution for w(t) we know that w=0 when "}}{INP_R 92 0 "> "{TEXT 0 14 "omega*t+phi=0;"}}{OUT_R 93 0 92{DAG =3+5*5n4 \`omega`j2x0001n3\`t`p6p6n3\`phi`p6j2x0000}}{COM_R 94 0{TEXT 1 237 "The next step is to look for the asymptotic solutions of x a nd y. First I plug the asymptotic solution for w into y'. Then \+ I attempt to solve y'=0 for c1. Again x' is not of interest here because it does not depend on any constants. "}}{INP_R 95 0 "> \+ "{TEXT 0 75 "(solve(\{ -x-(c1+3*(x -y)^2)*y +a*sqrt(lambda)*sin(o mega*t + phi)=0\},\{c1\}));"}}{OUT_R 96 0 95{DAG %2,2=3n3\`c1`*5+ Bn3\`x`i2x0001*5n3\`y`j2x0001p7j2x0002i2x0003*5p7pEpCp11j2x0006*3 pCj2x0003p13*7n3\`a`pEn4\`lambda`/3pEp11(3n3\`sin`,2+5*5n4\`omega `pEn3\`t`pEpEn3\`phi`pEpEpEpEpCp9}}{COM_R 97 0{TEXT 1 379 "\015No tice that if lambda is zero we would get the same equation for c1 as the graph above displays. This problem offers considerable \+ challenge because there are six variables too be considered inste ad of three as in the example above. A full analysis of this fu nction is tough but it is possible to fix some of the variables \+ in order to offer a glimpse at the behavior of c1. "}}{COM_R 98 0 {TEXT 1 512 "I chose to fix the variables to phi = 0 and lambda \+ =9, and use a=3 and omega=3/10 which are the values previously used. The value of c1 will oscillate with time. The new term i s the addition of another 1/y term that does not depend on positi on but is time dependent. At the special case where t=0 the grap h is the same as the one above. The graph is changed but is sti ll very similar. The constant phi will only change the initial p osition of the surface and not the overall form of the oscillatio n. l "}}{INP_R 99 0 "> "{TEXT 0 105 "animate3d( (-x-3*y*x^2 +6*x *y^2 -3*y^3 +9*sin(3/10*t))/y, x=-3..3 , y= -3..3 , t= 0..10/3*Pi ,frames=20);"}}{INP_R 100 0 "> "{TEXT 0 0 ""}}{INP_R 101 0 "> " {TEXT 0 0 ""}}{INP_R 102 0 "> "{TEXT 0 0 ""}}{INP_R 103 0 "> " {TEXT 0 0 ""}}{INP_R 104 0 "> "{TEXT 0 0 ""}}{INP_R 105 0 "> " {TEXT 0 0 ""}}}{END}