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In this contribution, the complicated dynamical behaviors and optimal harvesting policy of a discrete-time predator–prey model with fear and refuge effects are formulated. Both the fear and prey refuge effects refer to an interaction between predator and prey. In the first place, the existence and local stability of three fixed points of proposed model are investigated by virtue of our methodology, that is, the eigenvalues of the Jacobian matrix. One step further, it is worth mentioning that the model undergoes flip bifurcation (i.e., period–doubling bifurcation) and Neimark–Sacker bifurcation at the interior fixed point by the utilization of bifurcation theory and center manifold theory. Also, optimal harvesting strategy is investigated, and the expressions of optimal harvesting efforts are determined. Two examples, in the end, are put forward to prove that they are consistent with the previous theoretical results.

In this paper, we study Poincaré, Hopf and homoclinic bifurcations of limit cycles for planar near-Hamiltonian systems. Our main results establish Hopf and homoclinic bifurcation theories by higher order Melnikov functions, obtaining conditions on upper bounds and lower bounds of the maximum number of limit cycles. As an application, we concern a cubic near-Hamiltonian system, and study Hopf and homoclinic bifurcations in detail, finding more limit cycles than [26]. [ABSTRACT FROM AUTHOR]

We are interested in the global bifurcation diagram of radial solutions for the Gelfand problem with the exponential nonlinearity and a positive radially symmetric weight in the unit ball. When the weight is constant, it is known that the bifurcation curve has infinitely many turning points if the dimension 3 ≤ N ≤ 9 , and it has no turning points if N ≥ 10. In this paper, we show that the perturbation of the weight does not affect the bifurcation structure when 3 ≤ N ≤ 9. Moreover, we find a one-parameter family of radial singular solutions for a parametrized weight and study the Morse index of the singular solution. As a result, we prove that the perturbation affects the bifurcation structure in the critical dimension N = 10. Moreover, we give a classification of the bifurcation diagrams in the critical dimension. [ABSTRACT FROM AUTHOR]

In this paper, a bogie system with time delay is established. The centre manifold theorem and norm form theory are used to reduce the infinite dimensional delay system to the finite dimensional ordinary differential system, and the bifurcation behaviour of the bogie system is analysed. The MatCont toolkit was used to verify the subcritical bifurcation in the system. In addition, the influence of parameters on the bifurcation diagram of the system and the influence of parameters on the critical speed of the bogie system during the hunting motion are also analysed. [ABSTRACT FROM AUTHOR]

Bursting is a crucial form of firing in neurons, laden with substantial information. Studying it can aid in understanding the neural coding to identify human behavioral characteristics conducted by these neurons. However, the high-dimensionality of many neuron models imposes a difficult challenge in studying the generative mechanisms of bursting. On account of the high complexity and nonlinearity characteristic of these models, it becomes nearly impossible to theoretically study and analyze them. Thus, this paper proposed to address these issues by focusing on the midbrain dopamine neurons, serving as the central neuron model for the investigation of the bursting mechanisms and bifurcation behaviors exhibited by the neuron. In this study, we considered the dimensionality reduction of a high-dimensional neuronal model and analyzed the dynamical properties of the reduced system. To begin, for the original thirteen-dimensional model, using the correlation between variables, we reduced its dimensionality and obtained a simplified three-dimensional system. Then, we discussed the changing characteristics of the number of spikes within a burst by simultaneously varying two parameters. Finally, we studied the co-dimension-2 bifurcation in the reduced system and presented the bifurcation behavior near the Bogdanov-Takens bifurcation. [ABSTRACT FROM AUTHOR]

In ecology, the most significant aspect is that the interactions between predators and prey are extremely complicated. Numerous experiments have shown that both direct predation and the fear induced in prey by the presence of predators lead to a reduction in prey density in predator-prey interactions. In addition, a suitable shelter can effectively stop predators from attacking as well as support the persistence of prey population. There has been less exploration of the effects of not only fear but also refuge factors on the dynamics of predator prey interactions. In this paper, we unveil several conclusions about a predator-prey system with fuzzy parameters, considering the cost of fear in two prey species and the effect of shelter on two prey species and one predator. As the first step of the investigation, the boundedness and non-negativity of the solutions to the system are put forward. Using the Jocabian matrix and Lyapunov function methods, we further analyze the existence and stability of the available equilibria and also the existence of Hopf bifurcation, considering the fear parameter as the bifurcation parameter that has been observed by applying the normal form theory. Finally, numerical simulations help us better understand the dynamics of the model, in which some interesting chaotic phenomena are also exhibited.

We discuss main challenges of much-debated endovascular treatment in patients with “false” bifurcation stenoses of the left main coronary artery. There are no convincing literature data on the rationale of planning complete bifurcation stenting using 2 stents and clear indications for this procedure. We highlight the importance of studying the effectiveness and safety of the complex routine use of various intravascular imaging during the left main coronary artery percutaneous coronary intervention. We analyzed observations in which a “false” bifurcation lesion can only be considered an ostial stenosis, which will affect the stenting strategy. We focus on the development of universal algorithms for performing endovascular interventions, including those using intravascular imaging which role at each stage of surgery should be additionally studied.

Abstract We study the bifurcation curve and exact multiplicity of positive solutions in the space C 2 ( ( − L , L ) ) ∩ C ( [ − L , L ] ) $C^{2}\left ( (-L,L)\right ) \cap C\left ( [-L,L]\right ) $ for the Minkowski-curvature equation { − ( u ′ ( x ) 1 − ( u ′ ( x ) ) 2 ) ′ = λ f ( u ) , − L < x < L , u ( − L ) = u ( L ) = 0 . $$ \left \{ \textstyle\begin{array}{l} -\left ( \dfrac{u^{\prime }(x)}{\sqrt{1-\left ( {u^{\prime }(x)}\right ) ^{2}}}\right ) ^{\prime }=\lambda f(u),\text{\ \ }-L< x< L, \\ u(-L)=u(L)=0.\end{array}\displaystyle \right . $$ where λ > 0 $\lambda >0$ is a bifurcation parameter, f ∈ C [ 0 , ∞ ) ∩ C 2 ( 0 , ∞ ) $f\in C[0,\infty )\cap C^{2}(0,\infty )$ satisfies f ( u ) > 0 $f(u)>0$ for u > 0 $u>0$ and f is either concave or geometrically concave on ( 0 , ∞ ) $(0,\infty )$ . If f is a concave function, we prove that the bifurcation curve is monotone increasing on the ( λ , ∥ u ∥ ∞ ) $(\lambda ,\left \Vert u\right \Vert _{\infty })$ -plane. If f is a geometrically concave function, we prove that the bifurcation curve is either ⊂-shaped or monotone increasing on the ( λ , ∥ u ∥ ∞ ) $(\lambda ,\left \Vert u\right \Vert _{\infty })$ -plane under a mild condition. Some interesting applications are given.

Bursting is a crucial form of firing in neurons, laden with substantial information. Studying it can aid in understanding the neural coding to identify human behavioral characteristics conducted by these neurons. However, the high-dimensionality of many neuron models imposes a difficult challenge in studying the generative mechanisms of bursting. On account of the high complexity and nonlinearity characteristic of these models, it becomes nearly impossible to theoretically study and analyze them. Thus, this paper proposed to address these issues by focusing on the midbrain dopamine neurons, serving as the central neuron model for the investigation of the bursting mechanisms and bifurcation behaviors exhibited by the neuron. In this study, we considered the dimensionality reduction of a high-dimensional neuronal model and analyzed the dynamical properties of the reduced system. To begin, for the original thirteen-dimensional model, using the correlation between variables, we reduced its dimensionality and obtained a simplified three-dimensional system. Then, we discussed the changing characteristics of the number of spikes within a burst by simultaneously varying two parameters. Finally, we studied the co-dimension-2 bifurcation in the reduced system and presented the bifurcation behavior near the Bogdanov-Takens bifurcation.

Molecular biological networks are highly nonlinear systems that exhibit limit point singularities. Bifurcation analysis and multiobjective nonlinear model predictive control (MNLMPC) of a molecular network problem represented by the Pettigrew model were performed. The Matlab program MATCONT (Matlab continuation) was used for the bifurcation analysis and the optimization language PYOMO (python optimization modeling objects) was used for performing the multiobjective nonlinear model predictive control. MATCONT identified the limit points, branch points, and Hopf bifurcation points using appropriate test functions. The multiobjective nonlinear model predictive control was performed by first performing single objective optimal control calculations and then minimizing the distance from the Utopia point, which was the coordinate of minimized values of each objective function. The presence of limit points (albeit in an infeasible region) enabled the MNLMPC calculations to result in the Utopia solution. MNLMPC of the partial models also resulted in Utopia solutions.

Abstract This research paper investigates discrete predator-prey dynamics with two logistic maps. The study extensively examines various aspects of the system’s behavior. Firstly, it thoroughly investigates the existence and stability of fixed points within the system. We explores the emergence of transcritical bifurcations, period-doubling bifurcations, and Neimark-Sacker bifurcations that arise from coexisting positive fixed points. By employing central bifurcation theory and bifurcation theory techniques. Chaotic behavior is analyzed using Marotto’s approach. The OGY feedback control method is implemented to control chaos. Theoretical findings are validated through numerical simulations.

Abstract Background Bifurcation lesions are prevalent amongst patients with symptomatic coronary artery disease subjected to percutaneous coronary intervention (PCI). Recent consensus commends a conservative (provisional) approach when managing the side branch. Here, the aim was to explore the immediate impact of different bifurcation techniques (one stent and two stent strategies) on left ventricular LV) myocardial functions using speckle tracking echocardiography in patients subjected to elective PCI. Sixty two consecutive patients diagnosed with coronary bifurcation lesion (CBL) were enrolled. Patients were categorized into: one-stent strategy (Provisional group, n = 44) and a two-stent strategy (TAP, DK crush, or Culotte technique, n = 18), based on the coronary bifurcation site, angle, side branch diameter and Medina classification. LVEF%, regional and global longitudinal strain (GLS), and E/E' were measured before and within 24 h post PCI. Results In both provisional and 2- stent technique, the mitral inflow velocities and mitral annular velocities showed improvement with significant reduction in E/e' (P