📄 lvpp2d.mdl
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Points [0, 45]
DstBlock "Product"
DstPort 1
}
Branch {
DstBlock "Matrix Gain"
DstPort 1
}
}
}
Line {
SrcBlock "Sum"
SrcPort 1
DstBlock "Product"
DstPort 2
}
Annotation {
Position [167, 32]
Text "Lotka-Volterra Prey Predator Model Equation"
}
Annotation {
Position [343, 40]
Text "xdot = ax - bxy\nydot = -cy +dxy"
}
Annotation {
Position [435, 40]
Text "x = prey \ny = predator"
}
}
}
Block {
BlockType SubSystem
Name "lvpp2"
Ports [0, 1, 0, 0, 0]
Position [70, 131, 110, 189]
ShowPortLabels on
MaskType "Lotka Volterra System"
MaskDescription " This autonomous system represents the lotka vo"
"lterra prey predator model:\n xdot = ax - bxy; ydot = -cy +dxy\n where x r"
"epresents the prey and y represents the predator.\n Parameters and initial st"
"ate can be selected from the mask.\n"
MaskHelp " This autonomous system represents the lotka vo"
"lterra prey predator model.\n <p>\n The system equations are: \n xdot = ax -"
" bxy\n ydot = -cy +dxy\n where x represents the prey and y represents the pre"
"dator.\n Parameters and initial state can be selected from the mask.\n"
MaskPromptString "a|b|c|d|Initial point p0 = [x0 y0]"
MaskStyleString "edit,edit,edit,edit,edit"
MaskTunableValueString "on,on,on,on,on"
MaskCallbackString "||||"
MaskEnableString "on,on,on,on,on"
MaskVisibilityString "on,on,on,on,on"
MaskVariables "a=@1;b=@2;c=@3;d=@4;xy0=@5;"
MaskIconFrame on
MaskIconOpaque on
MaskIconRotate "none"
MaskIconUnits "autoscale"
MaskValueString "1|0.01|1|0.02|[30 60]"
System {
Name "lvpp2"
Location [437, 356, 988, 571]
Open off
ModelBrowserVisibility off
ModelBrowserWidth 200
ScreenColor "white"
PaperOrientation "landscape"
PaperPositionMode "auto"
PaperType "usletter"
PaperUnits "inches"
ZoomFactor "100"
AutoZoom on
Block {
BlockType Constant
Name "Constant"
Position [65, 146, 105, 164]
Value "[a -c]"
}
Block {
BlockType Integrator
Name "Integrator"
Ports [1, 1, 0, 0, 0]
Position [350, 134, 380, 156]
ExternalReset "none"
InitialConditionSource "internal"
InitialCondition "xy0"
LimitOutput off
UpperSaturationLimit "inf"
LowerSaturationLimit "-inf"
ShowSaturationPort off
ShowStatePort off
AbsoluteTolerance "auto"
}
Block {
BlockType SubSystem
Name "Matrix Gain"
Ports [1, 1, 0, 0, 0]
Position [165, 70, 225, 100]
Orientation "left"
ShowPortLabels on
MaskType "Matrix Gain"
MaskDescription "Matrix Gain."
MaskHelp "Multiplies input vector by entered matrix t"
"o produce output vector (y=Au)."
MaskPromptString "Gain matrix:"
MaskStyleString "edit"
MaskTunableValueString "on"
MaskEnableString "on"
MaskVisibilityString "on"
MaskVariables "K=@1;"
MaskDisplay "disp('[0 -b; d 0]')"
MaskIconFrame on
MaskIconOpaque on
MaskIconRotate "none"
MaskIconUnits "autoscale"
MaskValueString "[0 -b;d 0]"
System {
Name "Matrix Gain"
Location [162, 233, 402, 326]
Open off
ModelBrowserVisibility off
ModelBrowserWidth 200
ScreenColor "white"
PaperOrientation "landscape"
PaperPositionMode "auto"
PaperType "usletter"
PaperUnits "inches"
ZoomFactor "100"
AutoZoom on
Block {
BlockType Inport
Name "In1"
Position [25, 33, 55, 47]
Port "1"
PortWidth "-1"
SampleTime "-1"
DataType "auto"
SignalType "auto"
Interpolate on
}
Block {
BlockType StateSpace
Name "State\nSpace"
Position [80, 23, 145, 57]
ShowName off
A "[]"
B "[]"
C "[]"
D "K"
X0 "0"
}
Block {
BlockType Outport
Name "Out1"
Position [170, 33, 200, 47]
Port "1"
OutputWhenDisabled "held"
InitialOutput "[]"
}
Line {
SrcBlock "State\nSpace"
SrcPort 1
DstBlock "Out1"
DstPort 1
}
Line {
SrcBlock "In1"
SrcPort 1
DstBlock "State\nSpace"
DstPort 1
}
}
}
Block {
BlockType Product
Name "Product"
Ports [2, 1, 0, 0, 0]
Position [280, 119, 305, 166]
ShowName off
Inputs "2"
SaturateOnIntegerOverflow on
}
Block {
BlockType Sum
Name "Sum"
Ports [2, 1, 0, 0, 0]
Position [130, 145, 150, 165]
ShowName off
IconShape "round"
Inputs "++|"
SaturateOnIntegerOverflow off
}
Block {
BlockType Outport
Name "xy"
Position [445, 138, 475, 152]
Port "1"
OutputWhenDisabled "held"
InitialOutput "[]"
}
Line {
SrcBlock "Sum"
SrcPort 1
DstBlock "Product"
DstPort 2
}
Line {
SrcBlock "Integrator"
SrcPort 1
Points [15, 0]
Branch {
Points [0, -60; -150, 0]
Branch {
DstBlock "Matrix Gain"
DstPort 1
}
Branch {
Points [0, 45]
DstBlock "Product"
DstPort 1
}
}
Branch {
DstBlock "xy"
DstPort 1
}
}
Line {
SrcBlock "Product"
SrcPort 1
DstBlock "Integrator"
DstPort 1
}
Line {
SrcBlock "Matrix Gain"
SrcPort 1
Points [-20, 0]
DstBlock "Sum"
DstPort 1
}
Line {
SrcBlock "Constant"
SrcPort 1
DstBlock "Sum"
DstPort 2
}
Annotation {
Position [435, 40]
Text "x = prey \ny = predator"
}
Annotation {
Position [343, 40]
Text "xdot = ax - bxy\nydot = -cy +dxy"
}
Annotation {
Position [167, 32]
Text "Lotka-Volterra Prey Predator Model Equation"
}
}
}
Block {
BlockType SubSystem
Name "lvpp3"
Ports [0, 1, 0, 0, 0]
Position [70, 221, 110, 279]
ShowPortLabels on
MaskType "Lotka Volterra System"
MaskDescription " This autonomous system represents the lotka vo"
"lterra prey predator model:\n xdot = ax - bxy; ydot = -cy +dxy\n where x r"
"epresents the prey and y represents the predator.\n Parameters and initial st"
"ate can be selected from the mask.\n"
MaskHelp " This autonomous system represents the lotka vo"
"lterra prey predator model.\n <p>\n The system equations are: \n xdot = ax -"
" bxy\n ydot = -cy +dxy\n where x represents the prey and y represents the pre"
"dator.\n Parameters and initial state can be selected from the mask.\n"
MaskPromptString "a|b|c|d|Initial point p0 = [x0 y0]"
MaskStyleString "edit,edit,edit,edit,edit"
MaskTunableValueString "on,on,on,on,on"
MaskCallbackString "||||"
MaskEnableString "on,on,on,on,on"
MaskVisibilityString "on,on,on,on,on"
MaskVariables "a=@1;b=@2;c=@3;d=@4;xy0=@5;"
MaskIconFrame on
MaskIconOpaque on
MaskIconRotate "none"
MaskIconUnits "autoscale"
MaskValueString "1|0.01|1|0.02|[50 100]*0.9"
System {
Name "lvpp3"
Location [437, 356, 988, 571]
Open off
ModelBrowserVisibility off
ModelBrowserWidth 200
ScreenColor "white"
PaperOrientation "landscape"
PaperPositionMode "auto"
PaperType "usletter"
PaperUnits "inches"
ZoomFactor "100"
AutoZoom on
Block {
BlockType Constant
Name "Constant"
Position [65, 146, 105, 164]
Value "[a -c]"
}
Block {
BlockType Integrator
Name "Integrator"
Ports [1, 1, 0, 0, 0]
Position [350, 134, 380, 156]
ExternalReset "none"
InitialConditionSource "internal"
InitialCondition "xy0"
LimitOutput off
UpperSaturationLimit "inf"
LowerSaturationLimit "-inf"
ShowSaturationPort off
ShowStatePort off
AbsoluteTolerance "auto"
}
Block {
BlockType SubSystem
Name "Matrix Gain"
Ports [1, 1, 0, 0, 0]
Position [165, 70, 225, 100]
Orientation "left"
ShowPortLabels on
MaskType "Matrix Gain"
MaskDescription "Matrix Gain."
MaskHelp "Multiplies input vector by entered matrix t"
"o produce output vector (y=Au)."
MaskPromptString "Gain matrix:"
MaskStyleString "edit"
MaskTunableValueString "on"
MaskEnableString "on"
MaskVisibilityString "on"
MaskVariables "K=@1;"
MaskDisplay "disp('[0 -b; d 0]')"
MaskIconFrame on
MaskIconOpaque on
MaskIconRotate "none"
MaskIconUnits "autoscale"
MaskValueString "[0 -b;d 0]"
System {
Name "Matrix Gain"
Location [162, 233, 402, 326]
Open off
ModelBrowserVisibility off
ModelBrowserWidth 200
ScreenColor "white"
PaperOrientation "landscape"
PaperPositionMode "auto"
PaperType "usletter"
PaperUnits "inches"
ZoomFactor "100"
AutoZoom on
Block {
BlockType Inport
Name "In1"
Position [25, 33, 55, 47]
Port "1"
PortWidth "-1"
SampleTime "-1"
DataType "auto"
SignalType "auto"
Interpolate on
}
Block {
BlockType StateSpace
Name "State\nSpace"
Position [80, 23, 145, 57]
ShowName off
A "[]"
B "[]"
C "[]"
D "K"
X0 "0"
}
Block {
BlockType Outport
Name "Out1"
Position [170, 33, 200, 47]
Port "1"
OutputWhenDisabled "held"
InitialOutput "[]"
}
Line {
SrcBlock "In1"
SrcPort 1
DstBlock "State\nSpace"
DstPort 1
}
Line {
SrcBlock "State\nSpace"
SrcPort 1
DstBlock "Out1"
DstPort 1
}
}
}
Block {
BlockType Product
Name "Product"
Ports [2, 1, 0, 0, 0]
Position [280, 119, 305, 166]
ShowName off
Inputs "2"
SaturateOnIntegerOverflow on
}
Block {
BlockType Sum
Name "Sum"
Ports [2, 1, 0, 0, 0]
Position [130, 145, 150, 165]
ShowName off
IconShape "round"
Inputs "++|"
SaturateOnIntegerOverflow off
}
Block {
BlockType Outport
Name "xy"
Position [445, 138, 475, 152]
Port "1"
OutputWhenDisabled "held"
InitialOutput "[]"
}
Line {
SrcBlock "Constant"
SrcPort 1
DstBlock "Sum"
DstPort 2
}
Line {
SrcBlock "Matrix Gain"
SrcPort 1
Points [-20, 0]
DstBlock "Sum"
DstPort 1
}
Line {
SrcBlock "Product"
SrcPort 1
DstBlock "Integrator"
DstPort 1
}
Line {
SrcBlock "Integrator"
SrcPort 1
Points [15, 0]
Branch {
DstBlock "xy"
DstPort 1
}
Branch {
Points [0, -60; -150, 0]
Branch {
Points [0, 45]
DstBlock "Product"
DstPort 1
}
Branch {
DstBlock "Matrix Gain"
DstPort 1
}
}
}
Line {
SrcBlock "Sum"
SrcPort 1
DstBlock "Product"
DstPort 2
}
Annotation {
Position [167, 32]
Text "Lotka-Volterra Prey Predator Model Equation"
}
Annotation {
Position [343, 40]
Text "xdot = ax - bxy\nydot = -cy +dxy"
}
Annotation {
Position [435, 40]
Text "x = prey \ny = predator"
}
}
}
Line {
SrcBlock "Mux"
SrcPort 1
Points [20, 0]
Branch {
DstBlock "Selector1"
DstPort 1
}
Branch {
Points [0, -35]
DstBlock "Selector"
DstPort 1
}
Branch {
Points [0, 105]
DstBlock "Scope"
DstPort 1
}
}
Line {
Name "p1p2p3"
Labels [0, 0]
SrcBlock "Selector"
SrcPort 1
DstBlock "XYZ Graph"
DstPort 1
}
Line {
Name "v1v2v3"
Labels [0, 0]
SrcBlock "Selector1"
SrcPort 1
DstBlock "XYZ Graph"
DstPort 2
}
Line {
SrcBlock "Ground"
SrcPort 1
DstBlock "XYZ Graph"
DstPort 3
}
Line {
SrcBlock "lvpp1"
SrcPort 1
DstBlock "Mux"
DstPort 1
}
Line {
SrcBlock "lvpp2"
SrcPort 1
DstBlock "Mux"
DstPort 2
}
Line {
SrcBlock "lvpp3"
SrcPort 1
DstBlock "Mux"
DstPort 3
}
Annotation {
Position [74, 330]
HorizontalAlignment "left"
Text "See the effect of a small change in the initial"
" conditions."
}
}
}
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