SynopsisA function space approach is employed to obtain bifurcation functions for which the zeros correspond to the occurrence of periodic or aperiodic solutions near heteroclinic or homoclinic cycles. The bifurcation function for the existence of homoclinic solutions is the limiting case where the period is infinite. Examples include generalisations of Silnikov's main theorems and a retreatment of a singularly perturbed delay differential equation.

The pathobiology of atherosclerotic disease requires further elucidation to discover new approaches to address its high morbidity and mortality. To date, over 17 million cardiovascular-related deaths have been reported annually, despite a multitude of surgical and nonsurgical interventions and advances in medical therapy. Existing strategies to prevent disease progression mainly focus on management of risk factors, such as hypercholesterolemia. Even with optimum current medical therapy, recurrent cardiovascular events are not uncommon in patients with atherosclerosis, and their incidence can reach 10–15% per year. Although treatments targeting inflammation are under investigation and continue to evolve, clinical breakthroughs are possible only if we deepen our understanding of vessel wall pathobiology. Vascular smooth muscle cells (VSMCs) are one of the most abundant cells in vessel walls and have emerged as key players in disease progression. New technologies, including in situ hybridization proximity ligation assays, in vivo cell fate tracing with the CreERT2-loxP system and single-cell sequencing technology with spatial resolution, broaden our understanding of the complex biology of these intriguing cells. Our knowledge of contractile and synthetic VSMC phenotype switching has expanded to include macrophage-like and even osteoblast-like VSMC phenotypes. An increasing body of data suggests that VSMCs have remarkable plasticity and play a key role in cell-to-cell crosstalk with endothelial cells and immune cells during the complex process of inflammation. These are cells that sense, interact with and influence the behavior of other cellular components of the vessel wall. It is now more obvious that VSMC plasticity and the ability to perform nonprofessional phagocytic functions are key phenomena maintaining the inflammatory state and senescent condition and actively interacting with different immune competent cells.

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The objective of this study is to model the diagnostic transient waves in an integrated piezoelectric sensor/actuator plate with a view to using it as a first step towards establishing an entire structural health monitoring system and to provide experimental verification of the proposed models. PZT ceramic disks are surface mounted on an aluminum plate acting as both actuators and sensors to generate and collect A0 mode Lamb waves. Mindlin plate theory is adopted to model the propagating waves by taking both transverse shear and rotary inertia effects into account. Actuator and sensor models are both proposed. The interaction between an actuator and the host plate is modeled based on classical lamination theory. The converse piezoelectric effect of the actuator is treated as an equivalent bending moment applied to the host plate. The sensor acts as a capacitor that converts the sensed strain change into a voltage response. An analytical expression for the sensor output voltage in terms of the given input excitation signal is derived, and then experimental work is performed to verify the accuracy of the analytical model. Experimental results show that single-mode Lamb waves in the plate can be successfully generated and collected through the integrated PZT disks. The experiment also shows that the predicted sensor output for both amplitude and phase agrees well with experimentally collected data.