[Show abstract][Hide abstract] ABSTRACT: This book shows, for the very first time, how love stories — a vital issue in our lives — can be tentatively described with classical mathematics. Focus is on the derivation and analysis of reliable models that allow one to formally describe the expected evolution of love affairs from the initial state of indifference to the final romantic regime. The models are in full agreement with the basic philosophical principles of love psychology. Eight chapters are theoretically oriented and discuss the romantic relationships between important classes of individuals identified by particular psychological traits. The remaining chapters are devoted to case studies described in classical poems or in worldwide famous films.
[Show abstract][Hide abstract] ABSTRACT: We show in this paper that temporary bluffing has the power of promoting the transition from a bad to a good state in social systems. The analysis is carried out with reference to the simplest unit of interest in Sociology—the couple—but it can be certainly extended to larger social groups. More precisely, an already available mathematical model shows that couples composed of so-called secure individuals with neither too high nor too low appeals have two alternative romantic regimes—one satisfactory and one not. Thus, if one of these couples is trapped in its unsatisfactory regime the problem is how to escape from that trap and switch to the satisfactory regime. Temporary bluffing, namely, giving to the partner for a sufficiently long time a biased impression of the involvement or of the appeal, is a very effective, though not unique, way for performing the switch. This, in a sense, attenuates the negative moral value usually given to bluffing in social behavior.
[Show abstract][Hide abstract] ABSTRACT: Love stories are dynamic processes that begin, develop, and often stay for a relatively long time in a stationary or fluctuating regime, before possibly fading. Although they are, undoubtedly, the most important dynamic process in our life, they have only recently been cast in the formal frame of dynamical systems theory. In particular, why it is so difficult to predict the evolution of sentimental relationships continues to be largely unexplained. A common reason for this is that love stories reflect the turbulence of the surrounding social environment. But we can also imagine that the interplay of the characters involved contributes to make the story unpredictable-that is, chaotic. In other words, we conjecture that sentimental chaos can have a relevant endogenous origin. To support this intriguing conjecture, we mimic a real and well-documented love story with a mathematical model in which the environment is kept constant, and show that the model is chaotic. The case we analyze is the triangle described in Jules et Jim, an autobiographic novel by Henri-Pierre Roché that became famous worldwide after the success of the homonymous film directed by François Truffaut.
No preview · Article · Jun 2014 · Chaos (Woodbury, N.Y.)
[Show abstract][Hide abstract] ABSTRACT: A mathematical model is proposed for interpreting the love story between Elizabeth and Darcy portrayed by Jane Austen in the popular novel Pride and Prejudice. The analysis shows that the story is characterized by a sudden explosion of sentimental involvements, revealed by the existence of a saddle-node bifurcation in the model. The paper is interesting not only because it deals for the first time with catastrophic bifurcations in romantic relation-ships, but also because it enriches the list of examples in which love stories are described through ordinary differential equations.
Full-text · Article · Apr 2014 · Nonlinear Dynamics Psychology and Life Sciences
[Show abstract][Hide abstract] ABSTRACT: A mathematical model is proposed for interpreting the love story portrayed by Walt Disney in the film "Beauty and The Beast". The analysis shows that the story is characterized by a sudden explosion of sentimental involvements, revealed by the existence of a saddle-node bifurcation in the model. The paper is interesting not only because it deals for the first time with catastrophic bifurcations in specific romantic relationships, but also because it enriches the list of examples in which love stories are satisfactorily described through Ordinary Differential Equations.
Full-text · Article · Nov 2013 · International Journal of Bifurcation and Chaos
[Show abstract][Hide abstract] ABSTRACT: We develop a mathematical model for mimicking the love story between Scarlett and Rhett described in “Gone with the Wind”. In line with tradition in classical physics, the model is composed of two Ordinary Differential Equations, one for Scarlett and one for Rhett, which encapsulate their main psycho-physical characteristics. The two lovers are described as so-called insecure individuals because they respond very strongly to small involvements of the partner but then attenuate their reaction when the pressure exerted by the partner becomes too high. These characteristics of Scarlett and Rhett clearly emerge during the first part of the film and are sufficient to develop a model that perfectly predicts the complex evolution and the dramatic end of the love story. Since the predicted evolution of the romantic relationship is a direct consequence of the characters of the two individuals, the agreement between the model and the film supports the high credibility of the story. Although credibility of a fictitious story is not necessary from a purely artistic point of view, in most cases it is very appreciated, at the point of being essential in making the film popular. In conclusion, we can say that we have explained with a scientific approach why “Gone with the Wind” has become one of the most successful films of all times.
Full-text · Article · Aug 2013 · Physica A: Statistical Mechanics and its Applications
[Show abstract][Hide abstract] ABSTRACT: We show in this paper how simulations of ODEs and continuations of systems of algebraic
equations can be combined to study the evolution of biodiversity in multispecies systems where
phenotypic traits are genetically transmitted. We follow the adaptive dynamics (AD) approach,
which provides a deterministic approximation of the evolutionary dynamics of stationary coexisting
populations in terms of an ODE system, the so-called AD canonical equation. AD also provides
explicit conditions to test whether a stable evolutionary equilibrium of the canonical equation is
a branching point—resident and mutant morphs coexist and further differentiate, thus increasing
biodiversity—or not. We analyze a standard parameterized family of prey-predator communities,
described by the most standard ecological model, and propose an iterative procedure to obtain the
branching portrait, explaining the dependence of branching scenarios on two (demographic, environmental,
or control) parameters. Among a number of interesting results, in line with field studies and
known ecological principles, we find that prey branching is induced by the predation pressure, and
is favored when prey intraspecific competition is highly sensitive to the resident-mutant phenotypic
mismatch, while predator branching is not possible when prey and predators are present in an equal
number of morphs. This results in alternate prey-predator branching sequences with possible phases
of prey unilateral branching. The guidelines for deriving a general method for analyzing the evolution
of biodiversity are also discussed. The indications that can be obtained typically have a qualitative
nature, but can be of help for the long-term conservation and management of biodiversity.
Full-text · Article · Jan 2013 · SIAM Journal on Applied Mathematics
[Show abstract][Hide abstract] ABSTRACT: Plankton patchiness in homogeneous physical environments is studied in this paper assuming that all involved populations disperse diffusively. A recent but powerful sufficient condition for the emergence of spatial patterns in models with any number of species is systematically applied to all food chain and food web plankton models and the result is rather sharp: All models explicitly containing phytoplankton, zooplankton and planktivorous fish suggest zooplankton patchiness, while models not containing phytoplankton or fish populations do not. The results are in agreement with many previous but particular theoretical studies on plankton patchiness and Turing instability, and testable prediction of the models satisfying the sufficient predictions is that zooplankton should be more patchy then phytoplankton, a property that is often seen in natural settings. An application to a complex model with five compartments (nutrient, phytoplankton, zooplankton, planktivorous fish, carnivorous fish) highlights the predictive power of the method.
Full-text · Article · Oct 2012 · Theoretical Population Biology
[Show abstract][Hide abstract] ABSTRACT: The problem of the frequency of sexual intercourse in couples was investigated for the first time with a purely conceptual model. The model, based on a few axioms involving the notions of sexual appetite and erotic potential, was composed of two ordinary differential equations which turn out to be the same as those proposed almost one century ago in epidemiology. The model can be used to discuss the possibility of estimating strategic parameters from real data, as well as to criticize the rule of "the beans in the jar" proposed by Martin (1970).
Full-text · Article · May 2012 · Archives of Sexual Behavior
[Show abstract][Hide abstract] ABSTRACT: The emergence of inhomogeneities in the distributions of the abundances of spatially extended prey–predator systems is investigated. The method of analysis, based on the notion of diffusive (Turing) instability, is systematically applied to nine different models obtained by introducing an extra-factor into the standard Rosenzweig–MacArthur prey–predator model. The analysis confirms that the standard model is critical in the context of Turing instability, and that the introduction of any small amount of the extra-factor can easily promote or inhibit the emergence of spatial patterns.
[Show abstract][Hide abstract] ABSTRACT: A minimal model for the interactions of trees, insects, and their enemies suggests a simple formula for splitting all forests where insect outbreaks can occur into two categories: where outbreaks are periodic and endogenously generated and where outbreaks are triggered by exogenous factors and are, in general, recurrent but aperiodic. The formula is in full agreement with all field studies in which various phenomena triggering insect outbreaks have been identified. The observed consequences of introductions and removals of insects are also well predicted by the minimal model. But, even more surprisingly, the model allows a simple and explicit condition for the synchronization of outbreaks in spatially extended forests to be derived analytically. This condition is, in general, satisfied when the insect is a so-called pest, that is, when the outbreaks are extreme. The model also predicts the possibility of traveling waves of insect outbreaks.
No preview · Article · Aug 2011 · Theoretical Population Biology
[Show abstract][Hide abstract] ABSTRACT: Biological signal and image processing (BSIP) constitutes a major field of interest in both educational aspects and research environments in biomedical engineering. In fact, the physiological knowledge improvement in a wide variety of innovative research as well as the implementation in many clinical procedures extensively makes use of these concepts in more or less sophisticated medical applications. In this article, the important links between BSIP and physiological modeling and their important derived synergies are particularly stressed. In support of this aim, examples have been provided in the areas of cardiovascular system studies, as well as in neurosciences and functional imaging, by using different modalities. Along this direction, the integration operation of the detected information between multiple signals, organs, modalities, and across multiple scales (from gene/protein levels up to cell and organ levels) seems to be extremely promising. Further, advanced methods in the area of information treatment, such as time-frequency and time-variant approaches, have been investigated in the biomedical field together with the complexity measurements, most often carried out through nonlinear dynamical approaches where, also in this context, the integration between modeling and information processing plays a fundamental role. Finally, a few examples have been described in which the study of EMFs, in the form of signals and images properly detected, have a relevant impact on various biomedical applications.
[Show abstract][Hide abstract] ABSTRACT: Generally, physiological modeling and biomedical signal processing constitute two important paradigms of biomedical engineering (BME): their fundamental concepts are taught starting from undergraduate studies and are more completely dealt with in the last years of graduate curricula, as well as in Ph.D. courses. Traditionally, these two cultural aspects were separated, with the first one more oriented to physiological issues and how to model them and the second one more dedicated to the development of processing tools or algorithms to enhance useful information from clinical data. A practical consequence was that those who did models did not do signal processing and vice versa. However, in recent years,the need for closer integration between signal processing and modeling of the relevant biological systems emerged very clearly , . This is not only true for training purposes(i.e., to properly prepare the new professional members of BME) but also for the development of newly conceived research projects in which the integration between biomedical signal and image processing (BSIP) and modeling plays a crucial role. Just to give simple examples, topics such as brain–computer machine or interfaces,neuroengineering, nonlinear dynamical analysis of the cardiovascular (CV) system,integration of sensory-motor characteristics aimed at the building of advanced prostheses and rehabilitation tools, and wearable devices for vital sign monitoring and others do require an intelligent fusion of modeling and signal processing competences that are certainly peculiar of our discipline of BME.
[Show abstract][Hide abstract] ABSTRACT: The mean value of the catch and its variability due to environmental fluctuations are analyzed for a very general stock-recruitment model. Particular attention is devoted to the comparison of two standard fishing strategies (constant effort and constant escapement) in terms of mean catch, variance in catches, and maximum deviation of catch. It is demonstrated analytically that constant escapement policies should always give higher mean catch, but should give higher catch variance and more extreme catches only under certain conditions of environmental variability.
[Show abstract][Hide abstract] ABSTRACT: The relationships between cannibalism and pattern formation in spatially extended prey–predator systems are studied with a
model that degenerates, in the absence of cannibalism, into the most standard prey–predator model, known as Rosenzweig–MacArthur
model. The analysis is based on the theory developed long ago by Turing in his famous paper on morphogenesis, but in a special
form, which allows one to decouple the role of demographic parameters from that of diffusive dispersal. The proofs are given
in terms of prey and predator nullclines because ecologists are mainly familiar with this technique. The final result of the
analysis is that spatial pattern can exist only in systems with highly cannibalistic and highly dispersing predator provided
the attractor of the system in the absence of cannibalism is a limit cycle. This result is more simple and more complete than
that published in this journal a few years ago by Sun and coauthors.
KeywordsPrey–predator models–Spatial pattern–Turing instability–Cannibalism–Dispersal
[Show abstract][Hide abstract] ABSTRACT: We show in this paper that the analysis of diffusion-induced instability in spatially extended models can be performed by separating local dynamics from diffusion. This is possible not only in the case studied by Turing, namely models with two interacting variables, but also in the general case of three or more variables. The advantage of this decomposition, based on the notion of potential Turing instability, is illustrated through the analysis of two spatially extended plant–insect models.
Full-text · Article · Jan 2011 · Mathematical and Computer Modelling
[Show abstract][Hide abstract] ABSTRACT: Relationships between local stability and synchronization in networks of identical dynamical systems are established through the Master Stability Function approach. First, it is shown that stable equilibria of the local dynamics correspond to stable stationary synchronous regimes of the entire network if the coupling among the systems is sufficiently weak or balanced (in other words, stationary synchronous regimes can be unstable only if the coupling is sufficiently large and unbalanced). Then, it is shown that [de]stabilizing factors at local scale are [de]synchronizing at global scale again if the coupling is sufficiently weak or balanced. These results allow one to transfer, with almost no effort, what is known for simple prototypical models in biology and engineering to complex networks composed of these models. This is shown through a series of applications ranging from networks of electrical circuits to various problems in ecology and sociology involving migrations of plants, animal and human populations.
No preview · Article · Jul 2010 · Mathematical Biosciences and Engineering