Figure 1.1. Decline in Coho salmon stocks on the Thomson River, BC
Figure 1.2. Rate of decline on individual streams related to habitat variables
Figure 1.4. Compartment diagram of the bathtub model
Figure 1.6. Compartment diagram for the enzyme-mediated biochemical reaction
Figure 1.7. Graphical analysis of dv/dt = k1s − (k−1 + k2 + k1s)v
Figure 1.8. Compartment model for arsenic in rat hepatocytes
Figure 1.9. Compartment diagram for the IEUBK model for lead in children
Figure 1.10. A cartoon of the pogo stick or monopode
Figure 1.11. The monopode in stance phase
Figure 1.12. Diagram of the experimental fishpond system showing water flows between compartments
Figure 1.13. Compartment diagrams for Exercise 1.3
Figure 2.1. The standard size-class model
Figure 2.2. Stage-structured model for killer whales
Figure 2.3. Eigenvalue elasticities for stage-structured model for desert tortoise
Figure 2.4. Eigenvalue elasticities for stage-structured model for loggerhead sea turtles
Figure 2.7. Elasticity surface for the integral projection model for northern monkshood
Figure 3.1. Membrane-spanning channel with equivalent electrical circuit
Figure 3.3. Hypothetical energy landscape
Figure 3.4. Histogram from a computer experiment of tossing an unfair coin
Figure 3.5. Sums of exponentials fit to dwell time distributions of open states in an nAChR channel
Figure 3.7. Data from a series of voltage clamp measurements on a squid giant axon
Figure 3.9. Plots of the functions 1/[1 + exp(−v)] and 1/cosh(−v/2)
Figure 3.10. Voltage clamp currents in a barnacle muscle fiber
Figure 4.1. Schematic diagram of the repressilator
Figure 4.5. Graph of the function E(p) = −p + 18/(1 + p2) + 1
Figure 4.6. Diagram of the stability region for the repressilator system
Figure 4.7. Schematic diagram of bistable gene regulatory networks in bacteriophage λ
Figure 4.9. Bifurcation diagram of the (b, a) plane for the model [4.5]
Figure 4.10. Phase portrait of the (u, v) plane for the model [4.5] with (b, a) = (3, 1)
Figure 4.11. Phase portrait of the (u, v) plane for the model [4.5] with (b, a) = (3, 2)
Figure 5.1. Phase line of a one-dimensional differential equation with three equilibrium points
Figure 5.2. Plots of solutions x(t) to the differential equation
Figure 5.3. “Quiver plot” of the vector field defined by the differential equations [5.5]
Figure 5.5. Phase portraits of two-dimensional linear vector fields with a stable node and a saddle
Figure 5.7. Phase portraits of two-dimensional linear vector fields with a stable focus and a center
Figure 5.8. Limit set in a two-dimensional vector field
Figure 5.9. Nullclines for the Morris-Lecar model
Figure 5.13. Dynamics of system [5.22] along the x-axis for varying μ
Figure 5.14. The determinant of the Jacobian plotted as a function of v
Figure 5.15. Nullclines for the Morris-Lecar system for saddle-node parameter values
Figure 5.16. Phase portraits of the supercritical Hopf bifurcation for μ = −0.1 and 0.2
Figure 5.17. Phase portraits of the subcritical Hopf bifurcation for μ = −0.2 and 0.1
Figure 5.18. Phase portrait of the Morris-Lecar model with a single periodic orbit
Figure 5.19. Phase portraits of the Morris-Lecar system close to a saddle-node of periodic orbits
Figure 5.20. Phase portraits of the Morris-Lecar system close to a homoclinic orbit
Figure 6.1. Examples of epidemic curves
Figure 6.2. Deaths per week from plague in the island of Bombay 1905–1906
Figure 6.3. Graphical illustration that equation [6.5] has a unique solution between x = 0 and x = 1
Figure 6.7. Compartment diagram for discrete-event SIR model
Figure 6.8. Reported gonorrhea rate in the United States
Figure 6.10. Fraction of new HIV infections that are resistant to combination ARV treatment
Figure 6.11. Schematic depiction of the typical course of HIV infection in an adult
Figure 7.1. Depiction of particles undergoing a random walk on the line
Figure 7.2. Animal coat pattern of the eastern chipmunk
Figure 7.3. Insect color patterns: two beetles from the genus Anoplophora
Figure 7.4. Trajectories of the vector field [7.17]
Figure 7.5. Spiral patterns of the BZ reaction
Figure 7.6. Map of spiral wave in the (x, y) plane into the (c1, c2) concentration plane
Figure 7.7. Meandering paths of spiral cores in simulations of a reaction-diffusion system
Figure 8.2. Genealogies of successive dominant genotypes under low and high mutation rates
Figure 8.4. Relaxation oscillations in the van der Pol model [8.17] with C = 20
Figure 8.5. A simulation of the Helbing et al. (2000) model for exit panic
Figure 9.1. Outline of the modeling process
Figure 9.2. Outline of the steps in developing a model
Figure 9.3. Diagram of the compartments for soil organic matter in the CENTURY model
Figure 9.4. Compartment diagram of the model for TAME in the rat
Figure 9.5. Fitting a parametric rate equation model
Figure 9.6. Some widely used equations to fit nonlinear functional relationships
Figure 9.7. Cross-validation for linear versus quadratic regression
Figure 9.8. Examples of nonparametric rate equations based on data
Figure 9.11. The Doomsday model fitted to historical data on human population growth