In (a), ΔdV and there is only a single coral steady state for each value of dV. In (b) ΔdV >0 and alternative stable states exist for the values of dV between critC and critM, and an unstable equilibrium (dashed black line) exists between the two stable equilibria.</p
<p>For there is a region of bistability in which both trivial and non-trivial stable steady states ...
Bifurcations indicate qualitative changes in a system's behavior. For a dynamical system dy/dt=f(y,λ...
<p>Solid line indicates a branch of stable EPs, and dashed line indicates a branch of unstable EPs. ...
Bifurcation diagrams for (a) the unstructured macroalgae model, and (b) the stage-structured macroal...
<p>These diagrams, created using Xppaut, depict the occurrence of stable, equilibrium points (solid ...
<p>Combined bifurcation diagram, showing the dependence of the stationary solutions on both the degr...
<p>Tangent bifurcations are indicated by red stars. Stable and unstable equilibria branches are indi...
<p>Full and dashed lines correspond to stable and unstable solutions respectively. Parameter values ...
<p>Blue horizontal line indicates <i>b</i> = 0.05. Red curves represent stable steady states. This t...
<p>(a) case , (b) and (c) . Full and dashed lines correspond to stable and unstable solutions respe...
<p>These bifurcation diagrams illustrate the FP’s and PO’s of the <i>V</i> and <i>h</i> model states...
<p> The diagrams show the evolution of equilibria and oscillatory regimes for two values of the leak...
<p>The solid and dotted lines show the values at which the disease-free equilibrium point is stable ...
<p> and are complementary outputs, when one is high the other is low. Red (black) indicate stable (...
<p>In (<i>a</i>)–(<i>b</i>), the long-term behavior of the solutions is plotted as the strength of t...
<p>For there is a region of bistability in which both trivial and non-trivial stable steady states ...
Bifurcations indicate qualitative changes in a system's behavior. For a dynamical system dy/dt=f(y,λ...
<p>Solid line indicates a branch of stable EPs, and dashed line indicates a branch of unstable EPs. ...
Bifurcation diagrams for (a) the unstructured macroalgae model, and (b) the stage-structured macroal...
<p>These diagrams, created using Xppaut, depict the occurrence of stable, equilibrium points (solid ...
<p>Combined bifurcation diagram, showing the dependence of the stationary solutions on both the degr...
<p>Tangent bifurcations are indicated by red stars. Stable and unstable equilibria branches are indi...
<p>Full and dashed lines correspond to stable and unstable solutions respectively. Parameter values ...
<p>Blue horizontal line indicates <i>b</i> = 0.05. Red curves represent stable steady states. This t...
<p>(a) case , (b) and (c) . Full and dashed lines correspond to stable and unstable solutions respe...
<p>These bifurcation diagrams illustrate the FP’s and PO’s of the <i>V</i> and <i>h</i> model states...
<p> The diagrams show the evolution of equilibria and oscillatory regimes for two values of the leak...
<p>The solid and dotted lines show the values at which the disease-free equilibrium point is stable ...
<p> and are complementary outputs, when one is high the other is low. Red (black) indicate stable (...
<p>In (<i>a</i>)–(<i>b</i>), the long-term behavior of the solutions is plotted as the strength of t...
<p>For there is a region of bistability in which both trivial and non-trivial stable steady states ...
Bifurcations indicate qualitative changes in a system's behavior. For a dynamical system dy/dt=f(y,λ...
<p>Solid line indicates a branch of stable EPs, and dashed line indicates a branch of unstable EPs. ...