scholarly journals Oscillations in a simple climate–vegetation model

2015 ◽  
Vol 2 (1) ◽  
pp. 145-178
Author(s):  
J. Rombouts ◽  
M. Ghil

Abstract. We formulate and analyze a simple dynamical systems model for climate–vegetation interaction. The planet we consider consists of a large ocean and a land surface on which vegetation can grow. The temperature affects vegetation growth on land and the amount of sea ice on the ocean. Conversely, vegetation and sea ice change the albedo of the planet, which in turn changes its energy balance and hence the temperature evolution. Our highly idealized, conceptual model is governed by two nonlinear, coupled ordinary differential equations, one for global temperature, the other for vegetation cover. The model exhibits either bistability between a vegetated and a desert state or oscillatory behavior. The oscillations arise through a Hopf bifurcation off the vegetated state, when the death rate of vegetation is low enough. These oscillations are anharmonic and exhibit a sawtooth shape that is characteristic of relaxation oscillations, as well as suggestive of the sharp deglaciations of the Quaternary. Our model's behavior can be compared, on the one hand, with the bistability of even simpler, Daisyworld-style climate–vegetation models. On the other hand, it can be integrated into the hierarchy of models trying to simulate and explain oscillatory behavior in the climate system. Rigorous mathematical results are obtained that link the nature of the feedbacks with the nature and the stability of the solutions. The relevance of model results to climate variability on various time scales is discussed.

2015 ◽  
Vol 22 (3) ◽  
pp. 275-288 ◽  
Author(s):  
J. Rombouts ◽  
M. Ghil

Abstract. We formulate and analyze a simple dynamical systems model for climate–vegetation interaction. The planet we consider consists of a large ocean and a land surface on which vegetation can grow. The temperature affects vegetation growth on land and the amount of sea ice on the ocean. Conversely, vegetation and sea ice change the albedo of the planet, which in turn changes its energy balance and hence the temperature evolution. Our highly idealized, conceptual model is governed by two nonlinear, coupled ordinary differential equations, one for global temperature, the other for vegetation cover. The model exhibits either bistability between a vegetated and a desert state or oscillatory behavior. The oscillations arise through a Hopf bifurcation off the vegetated state, when the death rate of vegetation is low enough. These oscillations are anharmonic and exhibit a sawtooth shape that is characteristic of relaxation oscillations, as well as suggestive of the sharp deglaciations of the Quaternary. Our model's behavior can be compared, on the one hand, with the bistability of even simpler, Daisyworld-style climate–vegetation models. On the other hand, it can be integrated into the hierarchy of models trying to simulate and explain oscillatory behavior in the climate system. Rigorous mathematical results are obtained that link the nature of the feedbacks with the nature and the stability of the solutions. The relevance of model results to climate variability on various timescales is discussed.


2011 ◽  
Vol 356-360 ◽  
pp. 2430-2433 ◽  
Author(s):  
Fei Fan Zhang ◽  
Hua Yong Zhang ◽  
Tou Sheng Huang

From the holistic perspective, a new dynamic model is proposed in this research to investigate the interaction between vegetation growth and aeolian dust deposition. Three cases of equilibrium distribution can be obtained and the stability of interior equilibriums is determined. When there is a stable interior equilibrium, a critical curve exists and separates the coexistent area where vegetation can survive in the environment of aeolian dust deposition, from the other area where vegetation is to be excluded. Simulation analysis further reveals the variation of the critical curve with the parameters and the anthropic influences. The critical curve and the coexistent equilibrium described by the model may be used as a theoretical basis to evaluate the feasibility of vegetation restoration in the environment of aeolian dust deposition.


2014 ◽  
Vol 07 (01) ◽  
pp. 1450008 ◽  
Author(s):  
J. B. SHUKLA ◽  
ASHISH GOYAL ◽  
P. K. TIWARI ◽  
A. K. MISRA

In this paper, a nonlinear mathematical model is proposed and analyzed to study the role of dissolved oxygen (DO)-dependent bacteria on biodegradation of one or two organic pollutant(s) in a water body. In the case of two organic pollutant(s), it is assumed that the one is fast degrading and the other is slow degrading and both are discharged into the water body from outside with constant rates. The density of bacteria is assumed to follow logistic model and its growth increases due to biodegradation of one or two organic pollutant(s) as well as with the increase in the concentration of DO. The model is analyzed using the stability theory of differential equations and by simulation. The model analysis shows that the concentration(s) of one or both organic pollutant(s) decrease(s) as the density of bacteria increases. It is noted that for very large density of bacteria, the organic pollutant(s) may be removed almost completely from the water body. It is found that simulation analysis confirms the analytical results. The results obtained in this paper are in line with the experimental observations published in literature.


2020 ◽  
pp. 1-36
Author(s):  
Antoine Le Riche

This paper analyzes the impact of trade on the stability properties of trading countries and on stationary welfare. We consider a two-country two-good two-factor overlapping generations model where countries differ in terms of their technology. In the autarky equilibrium and the free-trade equilibrium, indeterminacy relies, under dynamic efficiency, on a capital intensive consumption good and intermediate values of the elasticity of intertemporal substitution in consumption. Opening the borders to trade can be a source of a global destabilizing effect. Indeed, considering a free-trade equilibrium in which one country is an exporter of the consumption good and the other country is an exporter of the investment good, indeterminacy can occur with trade even though the two countries are determinate in autarky. Finally, opening to trade increases the stationary welfare of the country that exports the investment good and deteriorates the one of the other country.


1925 ◽  
Vol 8 (2) ◽  
pp. 183-188 ◽  
Author(s):  
P. A. Levene ◽  
M. H. Pfaltz
Keyword(s):  

1. The tripeptide glycyl-levo-alanyl-glycine in solution of either one or ten equivalents of alkali does not undergo racemization on standing. 2. The dipeptide levo-alanyl-glycine under the conditions given in (1) does not undergo racemization. 3. In ketopiperazines, levo-alanyl-glycine anhydride and in levo-prolyl-glycine anhydride under the influence of dilute alkalies, racemization takes place. 4. Racemization in the present experiments was never complete. The degree of racemization seems to depend, on the one hand, on the stability of the ketopiperazine ring; on the other, on the concentration of the alkali. 5. The significance of these observations will depend on the outcome of the work on a larger number of polypeptides and ketopiperazines. The work is now in progress in this laboratory.


1983 ◽  
Vol 48 (2) ◽  
pp. 364-378 ◽  
Author(s):  
Rolf Voigtländer ◽  
Jaromír Hlavatý ◽  
Jiří Volke ◽  
Viktor Bakos

The last two compounds in a 5-membered series of aromatic dinitro compounds are reduced in a completely different manner at mercury electrodes. 2,2'-Dinitrodiphenylmethane (I) - in which a conjugation of both symmetrical moieties is ruled out - is electrolytically reduced in an eight-electron step to a bishydroxylamine this being most stable between pH 4.5 and 5.0. In processing the catholyte increase in concentration of this product leads to its intermolecular disproportionation, resulting in the formation of dibenzo[b, e]-1,2-diazepine 5-oxide (IV) and 2,2'-diaminodiphenylmethane (III). 2,2'-Dinitrobenzophenone (II) reduces at more positive potentials. Its preparative electrolysis in acetonitrile (with 0.1M-N(n-C4H9)4PF6 as supporting electrolyte) the application of which was made necessary by the low solubility of II in ethanol, proceeding in an anomalous way. In the most positive cathodic wave a radical anion results, the following cathodic wave corresponds to a 6-electron reduction of the one nitro group to an amino group while the other nitro group splits off as the anion NO-2 (this later giving an anodic wave). Its formation has been proved by standard addition in polarography and by a qualitative analytical test. The product which results through this electrode process and a follow-up chemical reaction is acridone. This in turn, reduces in the third, most negative 4-electron wave to dihydroacridine. The comparison of all substances studied in this series reveals that their reducibility decreases with respect to the link X, viz. in the sequence CO > O > S and CH2 > NH. The electrolytical reduction on mercury cathodes occurs in a similar manner with analogues where X = O, S or CH2. Here, the main intermediate is the bis-hydroxylamine the stability of which predetermines the structure of final products. The other group comprises the substances with X = CO and NH. Here the main intermediate is the 2-nitro-2'-amino-diphenyl-X which is formed in a 6-electron process taking place at one of the nitro groups. The follow-up cyclization reaction leading to seven-membered heterocyclic rings located between two benzene nuclei only occurs with analogues of the type X = CH2, O and S. A partial reduction of dinitro compounds of this series has been observed with the analogue containing the NH link although that with X = CO has generally good preconditions for this mechanism.


The present paper contains some further developments of the theory of the moon, which are given at length, in order to save the trouble of the calculator, and to avoid the danger of mistake. The author remarks, that while it seems desirable, on the one hand, to introduce into the science of physical astronomy a greater degree of uniformity, by bringing to perfection a theory of the moon founded on the integration of the equations employed in the planetary theory, it is also no less important, on the other hand, to complete, in the latter, the method hitherto applied solely to the periodic inequalities. Hi­therto those terms in the disturbing function which give rise to the secular inequalities, have been detached, and the stability of the system has been inferred by means of the integration of certain equations, which are linear when the higher powers of the eccentri­cities are neglected and from considerations founded on the varia­tion of the elliptic constants. But the author thinks that the stability of the system may be inferred also from the expressions which result at once from the direct integration of the differential equations. The theory, he states, may be extended, without any analytical difficulty, to any power of the disturbing force, or of the eccentricities, ad­mitting the convergence of the series; nor does it seem to be limited by the circumstance of the planet’s moving in the same direction.


1860 ◽  
Vol 7 (35) ◽  
pp. 1-23 ◽  

The new position in which you have done me the honour this day to place me, entails upon me the duty of passing in review the varied interests and difficult problems of social and medical science, which are necessarily involved in promoting that which is the primary object of this Association, the welfare of the insane. The welfare of the insane! What a world of interests does not this small phrase include; what questions of individual happiness or misery; what questions of the prosperity or ruin of families; what questions of morality and law, of religion and politics; in fine, does it not ‘inferentially include the welfare of the human race. From time when Nebuchadnezzar ate grass, the happiness of the human race has often been at the mercy of the not metaphorical insanity of its rulers; and how often does not madness in lower stations imperil all that is precious. A mad orator on the floor of the house, or in the pulpit, may do comparatively little mischief, for opinion breaks no bones; but madness in a man of action, in an admiral for instance who commits suicide in the heat of an engagement, or an engineer in charge of a railway train; to what fearful disasters may it not give rise? In the world there is nothing great but man, in man there is nothing great but mind, says Hamilton. How vast, how wonderful a subject of study, therefore, is mind, whether in its integrity, or its decadence and ruin, in its health or its disease! Mental physicians, are we pledged to devote ourselves to the contemplation, and, as far as may be, to the full appreciation of this great subject, that we may oppose decay, and relieve disease ? Would it were possible to prevent it! Mental hygiene is, indeed, a subject vast as that of human progress. The highest and lowest stages of human development, those of the savage and the practical philosopher, are, perhaps, almost equally free from this direst scourge of human pride; the one with passions undeveloped, the other with passions under subjection. But the line of progress from one to the other of these termini, is strewn with those who have fallen in their weakness to linger and to die. Madness, the Nemesis of that ill-directed, ill-regulated development that we call civilization, what if it were to increase until the tendencies to mental disease overweighed in the community the conservative powers of health! There have been communities and times in which physical disease has threatened, or actually put an end to a race of men; and there have been communities and times in which folly and passion and delusion have been so widely endemic, that the fabric of society has been torn down, and even its very foundations shaken; and were it not for the resiliency of nature, the benign law of adjustment, by which deviations from law are a check upon further deviation, it is possible to conceive that the tendencies to mental infirmity and disease should increase; that passionate selfishness and insane folly should have continually augmenting power to reproduce themselves until acquired, and hereditary tendencies to madness should overbalance the forces of self-control and sanity, so that an observer, neither cynical nor metaphorical, might justly exclaim upon the “mad world,” and races, like families, become impotent for all except mischief and disaster, until time, the great physician, brought the only cure in extinction. Such speculations as these are not without their use, impossible as their realization may appear; they at least serve to make us value rightly the blessings we enjoy, blessings which from their commonness we are too apt to over look. We have no earthquakes in this country, and we calculate upon the stability of our buildings; we have no dead calms, and that world without motion, whose stagnant putridity has been painted by Byron and Coleridge, is to us a dread but impossible imagining. But the stability of our dwelling-place, and the restless agitation of the elements, although among those simple elementary conditions upon which our being depends, are also conditions which it is most easy to conceive might have been otherwise.


Author(s):  
N. A. Ablyatipova ◽  
E. A. Ashurova

For the Russian reality, the stability and stability of the execution of transactions and obligations in the context of frequent and unpredictable changes in the external environment is becoming an increasingly important component of economic and legal relations. Modern civil legislation, on the one hand, guarantees the stability of existing legal relations, on the other, allows for the modification and termination of contracts both at the mutual desire of the parties, and in connection with the will of the other party, if it is granted such a right. The third option is a way to change or terminate the contract in court. However, at present, there are many subjective and objective circumstances that are not provided for by the parties when concluding the contract, which make it difficult or even impossible to continue performing obligations under it while maintaining the conditions that were originally laid down in it. Not always resolving of such situations envisaged by the legislator, but because there are situations when the parties relations are further complicated by the inability to quickly and effectively solve the current conflict, especially if parties are business entities and any delay can lead to significant financial costs not only of the parties of legal relations, but also third parties whose rights are directly or indirectly affected.


Author(s):  
Mary Elise Sarotte

This chapter addresses why November 1989 became the moment that the models for the future were launched. By the night of November 9, five developments had permanently altered the Cold War and produced a causal chain that resulted in the unintentional opening of the Berlin Wall. The nature of this causal chain suggests that theorists of power and theorists of ideas need to pay attention to each other to understand what happened. On the one hand, some developments were based on old-fashioned realist calculations. On the other hand, some developments were ones of attitude rather than capability, of ideas rather than material abilities. In the course of 1989, half of Europe had come to the conclusion that it need not continue to live under nondemocratic regimes in the interest of maintaining the stability of the whole.


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